How many feet of chain fence are necessary to enclose a dog pen that is square and has an area of 64 square feet?
Doing this, we get that 32 feet are needed.
Square:
The area of a square of side s is:
[tex]A = s^2[/tex]
And the perimeter is:
[tex]P = 4s[/tex]
Area of 64 square feet
This means that:
[tex]s^2 = 64[/tex]
[tex]s = \sqrt{64}[/tex]
[tex]s = 8[/tex]
The side of the square is of 8 feet.
Perimeter:
Side of 8 feet, so:
[tex]P = 4s = 4(8) = 32[/tex]
32 feet of chain fence are needed.
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Identify the slope of the line shown in the graph below:
An amusement park charges $9.00 for admission $4.00 per ride. Write an equation that gives the cost in dollars as a function of number of rides
T = total cost
X= number of rides
T=4.00x+9.00
Please solve for c :3
3c - 2 = 5(c+2)
At 1:00 p.m. a car leaves st. louis for chicago, traveling at a constant speed of 65 miles per hour. at 2:00 p.m. a truck leaves chicago for st. louis, traveling at a constant speed of 55 miles per hour. if it is a 305-mile drive between st. louis and chicago, at what time will the car and truck pass each other?
To find out when the car and truck will pass each other, set up an equation where the sum of the distances covered by each at their respective speeds equals 305 miles. After solving, it's determined they will pass each other at 4:00 p.m.
To determine at what time the car and truck will pass each other, we need to calculate how far each vehicle will have traveled before they meet. The car leaves St. Louis at 1:00 p.m., while the truck leaves Chicago at 2:00 p.m., one hour later. We assume they meet after the car has been traveling for t hours and the truck for t - 1 hours.
The distance the car travels is the product of its speed and time, which can be calculated as 65 miles per hour times t hours. The truck's distance is 55 miles per hour times (t - 1) hours. Since the total distance between St. Louis and Chicago is 305 miles, we combine these distances to form the equation:
65t + 55(t - 1) = 305
Solving this equation:
65t + 55t - 55 = 305120t - 55 = 305120t = 305 + 55120t = 360t = 360 / 120t = 3 hoursSince the car has been traveling for 3 hours after 1:00 p.m., the two vehicles will pass each other at 4:00 p.m.
A choir has 3 spots open for altos, and 8 altos are interested in them. In how many ways can the open spots be filled?
There are total 56 ways to fill the open spot .
What is combination?
A combination is a way for determining the number of possible arrangements in a collection of items where the order of selection does not matter.
Formula for combination[tex]C(n, r) =\frac{n!}{(n - r)!r!}[/tex]
where,
n is the number of items in set.
r is the number of items selected from the set.
According to the question we have,
Number of altos, n = 8
Number of open spots, r = 3
Therefore, the number of ways to fill open spots = C(8, r)
Number of ways = [tex]\frac{8!}{3!(8-3)!}[/tex]
Number of ways = [tex]\frac{8!}{5!3!}[/tex][tex]= \frac{(8)(7)(6)(5!)}{5!3!}[/tex] = [tex]\frac{(8)(7)(6)}{(3)(2)} =8(7) = 56[/tex]
Hence, there are total 56 ways to fill the open spot .
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Find the inverse
f(x) = [tex] \frac{x}{x + 2} [/tex]
In the diagram, is the perpendicular bisector of and is also the angle bisector of . If m = x, which quantity is equal to sin ?
The quantity equal to sin ∠DPB is sin(x/2), corresponding to option B.
In the given diagram, overline PN serves as the perpendicular bisector of overline AB, implying that point N lies on the midpoint of segment AB.
Additionally, overline PN functions as the angle bisector of ∠CPD. Since ∠CPD measures x degrees, by the angle bisector theorem, ∠DPN and ∠DPB each measure x/2 degrees.
Now, to determine sin ∠DPB, we consider the right triangle DPN. By definition, sin θ = opposite/hypotenuse.
In this triangle, the opposite side to ∠DPB is overline DN, and the hypotenuse is overline DP.
Therefore, sin ∠DPB = DN/DP.
Since ∠DPN = x/2, applying trigonometric ratios in right triangle DPN, sin(x/2) = DN/DP.
Hence, the quantity equal to sin ∠DPB is sin(x/2), corresponding to option B.
The probable question may be:
In the diagram, overline PN is the perpendicular bisector of overline AB and is also the angle bisector of ∠ CPD If m∠ CPD=x , which quantity is equal to sin ∠ DPB ?
A. sin π /2
B. sin x/2
C. cos x/2
D. cos π /3
Is the value of [tex] \sqrt{42} [/tex] a rational or irrational number? Is it's value between 3 and 5, 5 and 7, or 7 and 9?
Marie is taking a test that contains a section of 10 true-false questions. How many of the possible groups of answers to these questions have at least 5 correct answers of true? Hint: Assign the variable x in the binomial expansion to be the number of true answers and y to be the number of false answers.
To solve this problem, we use the combination equation to find for the possible groups of answer to the questions. Since we are looking for at least 5 correct answers out of 10 questions, therefore we find for 10 ≥ r ≥ 5. We use the formula for combination:
nCr = n! / r! (n – r)!
Where,
n = total number of questions = 10
r = questions with correct answers
For 10 ≥ r ≥ 5:
10C5 = 10! / 5! (10 – 5)! = 252
10C6 = 10! / 6! (10 – 6)! = 210
10C7 = 10! / 7! (10 – 7)! = 120
10C8 = 10! / 8! (10 – 8)! = 45
10C9 = 10! / 9! (10 – 9)! = 10
10C10 = 10! / 10! (10 – 10)! = 1
Summing up all combinations will give the total possibilities:
Total possibilities = 252 + 210 + 120 + 45 + 10 + 1 = 638
Answer: 638
Write an algebraic expression for 4 more than p
What is 65 percent converted into a fraction in simplest form\?
On a multiple choice test with 13 questions, each question has four possible answers, one of which is correct. for students who guess at all answers, find the standard deviation for the number of correct answers.
Circle A and circle B are congruent. CD is a chord of both circles. If AB = 8 ft and CD = 6 ft, how long is a radius?
Let us say that the intersection point of lines AB and CD is called point E. The lines AB and CD are perpendicular to each other which also means that the triangle CEB is a right triangle.
Where the line CB is the radius of the circle while the side lengths are half of the whole line segment:
EB = 0.5 AB = 0.5 (8 ft) = 4 ft
CE = 0.5 CD = 0.5 (6 ft) = 3 ft
Now using the hypotenuse formula since the triangle is right triangle, we can find for the radius or line CB:
CB^2 = EB^2 + CE^2
CB^2 = (4 ft)^2 + (3 ft)^2
CB^2 = 16 ft^2 + 9 ft^2
CB^2 = 25 ft^2
CB = 5 ft = radius
Answer:
5ft
Step-by-step explanation:
Given f(x) = x2 + x − 2 and g(x) = 2x − 4, identify (f + g)(x).
4 workers get paid 160,000 for working for five days, how much will 5 workers get paid for working for a day
There are 20 wild pigs on an island and the number of pigs doubled each year for the past 5 years. The independent variable is
Answer:
The independent variable is time.
Step-by-step explanation:
Given,
The original number of pigs on the island = 20,
Also, the number of pigs doubled each year,
After 1 year the pigs = 20(2),
After 2 years = 20(2)²,
After 3 years = 20(2)³,
......................., so on...
Similarly, the number of pigs after t years would be,
[tex]y=20.2^t[/tex]
⇒ The value of y depends upon t,
⇒ The number of pigs depends upon the time ( in years ),
Since, the variable in which the other variable depends is called independent variable,
Hence, the independent variable must be time.
HELP If f(x)=15x+3, then f^-1(x)=?
The inverse of the function f(x) = 15x + 3 is found by swapping x and f(x) in the equation and solving for f^-1(x), which leads to f^-1(x) = (x - 3) / 15.
Explanation:To find the inverse of the function f(x) = 15x + 3, it is necessary to first swap x and f(x) in the function equation. This results in x = 15f^-1(x) + 3. Secondly, solving for f^-1(x) means isolating this on one side of the equation. That results in f^-1(x) = (x - 3) / 15.
So, the inverse function of f(x) = 15x + 3 is f^-1(x) = (x - 3) / 15.
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Please, would somebody help me solve this math problem? I have no idea how to solve it.
Create a set of numbers where:
the mode is equal to 10
the median is equal to 12
the average is 12
The manager of a baseball team has 15 players to choose from for his nine person batting order. How many different ways can he arrange the players in the lineup. A.5005. B.362880. C.3603600. D.1816214400
Answer: D. 1816214400
Step-by-step explanation:
When we select r things from n things in order we apply permutations and the number of ways to select r things = [tex]^nP_r=\dfrac{n!}{(n-r)!}[/tex]
Given : Total player = 15
Required number of players for Batting order = 9
Then the number of different ways to select 9 person batting order so that he arrange the players in the lineup would be [tex]^{15}P_9=\dfrac{15!}{(15-9)!}[/tex]
[tex]=\dfrac{15\times14\times13\times12\times11\times10\times9\times8\times7\times6!}{6!}[/tex]
[tex]=1816214400[/tex]
∴ The number of different ways can he arrange the players in the lineup = 1816214400
Hence, the correct answer is D. 1816214400
Solve for x..
a) x= 8
B) x= 22.5
C) x= 32.4
D) x= 40.5
A color printer prints 31 pages in 12 minutes. how many minutes does it take per page?
The function $f : \mathbb{r} \rightarrow \mathbb{r}$ satisfies $f(x) f(y) - f(xy) = x + y$ for all $x$, $y \in \mathbb{r}$. find $f(x)$.
The area of a parallelogram is modeled by the formula, A = lw. Solve the equation for w.
A. w=Al
B. w=I/A
C. w=A/I
D. w=2AI
Answer:
.C
Step-by-step explanation:
Which polynomial is a perfect square trinomial? (1 point) 49x2 − 28x + 16 4a2 − 20a + 25 25b2 − 20b − 16 16x2 − 24x − 9?
Solve for x.5(x – 10) = 30 – 15x
Answer:
x=4
Step-by-step explanation:
We know that y=mx+b is the formula we use for lines. Is the value of "m" considered to be a term, a coefficient or a factor?
Question 3 options:
Term
Coefficient
Factor
Find two geometric means between 10 and 1250.
(05.01 MC)
The table and the graph each show a different relationship between the same two variables, x and y:
A table with two columns and 5 rows is shown. The column head for the left column is x, and the column head for the right column is y. The row entries in the table are 3,210 and 4,280 and 5,350 and 6,420. On the right of this table is a graph. The x axis values are from 0 to 10 in increments of 2 for each grid line. The y axis values on the graph are from 0 to 550 in increments of 110 for each grid line. A line passing through the ordered pairs 2, 110 and 4, 220 and 6, 330 and 8, 440 is drawn.
How much more would the value of y be in the table than its value on the graph when x = 11?
100
165
395
440
The value of y in the table is 165 more than the value of y in the graph
The points on the table are represented as:
(3,210) and (4,280)So, the equation of the table is calculated using:
[tex]y = \frac{y_2 -y_1}{x_2 -x_1}(x -x_1) + y_1[/tex]
This gives
[tex]y = \frac{280 - 210}{4 - 3} (x - 3) + 210[/tex]
[tex]y = 70(x - 3) + 210[/tex]
Expand
[tex]y = 70x - 210 + 210[/tex]
[tex]y = 70x [/tex]
When x = 11,
We have:
[tex]y = 70 \times 11[/tex]
[tex]y = 770[/tex]
The points on the graph are represented as:
(2,110) and (4,220)So, the equation of the graph is calculated using:
[tex]y = \frac{y_2 -y_1}{x_2 -x_1}(x -x_1) + y_1[/tex]
This gives
[tex]y = \frac{220 - 110}{4 - 2} (x - 2) + 110[/tex]
[tex]y = 55 (x - 2) + 110[/tex]
Expand
[tex]y = 55x - 110 + 110[/tex]
[tex]y = 55x[/tex]
When x = 11,
We have:
[tex]y = 55 \times 11[/tex]
[tex]y = 605[/tex]
Calculate the difference between the y-values
[tex]y_2 - y_2 =770 - 605[/tex]
[tex]y_2 - y_2 =165[/tex]
Hence, the value of y in the table is 165 more than the value of y in the graph
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