Answer:
327 children and 318 adults
Step-by-step explanation:
The x be the amount of children and y be the amount of adults that were at the swimming pool. We can use this to set up a system of equations:
x+y=645
1.75x+2.50y=1367.25
Move y to the other side in the first equation to isolate x and solve the system using substitution:
x=645-y
1.75(645-y)+2.50y=1367.25
Distribute
1128.75-1.75y+2.50y=1367.25
1128.75+0.75y=1367.25
Subtract 1128.75 from both sides
0.75y=238.5
Divide both sides by 0.75
y=318
x=645-y
x=645-318
x=327
327 children and 318 adults swam at the pool that day
Sally earns $30 for 3 hours of babysitting. How much will she earn for 6 hours?
How much would she earn for 9 hours?
Answer:
6 hours-$60
9 hours-$90
Step-by-step explanation:
$10 an hour
Answer:
My hypothesis is she will earn $60 dollars for 6 hours and for 9 hours she will make $90 because she gets paid $10 each hour I believe so.
Step-by-step explanation:
the 4. In the figure, find length of side A AB. 17 15 ph
Answer:
8
Step-by-step explanation:
Look like BC is 15 and AC is 17
The Pythagorean Theorem states that a^2 + b^2 = c^2
so AC^2 = AB^2 + BC^2
17^2 = AB^2 + 15^2
289 = AB^2 + 225
AB^2 = 64
AB = 8
evaluate the definite integral from pi/3 to pi/2 of (x+cosx) dx
Answer:
[tex]0.8194[/tex]
Step-by-step explanation:
[tex]\int\limits^\frac{\pi}{2} _\frac{\pi}{3} {x+cos(x)} \, dx\\\\=\frac{1}{2}x^2+sin(x)\Bigr|_{\frac{\pi}{3}}^{\frac{\pi}{2}}\\\\=[\frac{1}{2}(\frac{\pi}{2})^2+sin(\frac{\pi}{2})]-[\frac{1}{2}(\frac{\pi}{3})^2+sin(\frac{\pi}{3})]\\\\=[\frac{1}{2}(\frac{\pi^2}{4})+1]-[\frac{1}{2}(\frac{\pi^2}{9})+\frac{\sqrt{3}}{2}]\\ \\ =\frac{\pi^2}{8}-\frac{\pi^2}{18}+1-\frac{\sqrt{3}}{2}\\ \\ \approx0.8194[/tex]
Answer:
[tex]\displaystyle \int\limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} {(x + \cos x)} \, dx = \frac{5 \pi ^2}{72} + 1 - \frac{\sqrt{3}}{2}[/tex]
General Formulas and Concepts:
Calculus
Integration
IntegralsIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
Identify.
[tex]\displaystyle \int\limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} {(x + \cos x)} \, dx[/tex]
Step 2: Integrate
[Integral] Rewrite [Integration Property - Addition/Subtraction]: [tex]\displaystyle \int\limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} {(x + \cos x)} \, dx = \int\limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} {x} \, dx + \int\limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} {\cos x} \, dx[/tex][Left Integral] Integration Rule [Reverse Power Rule]: [tex]\displaystyle \int\limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} {(x + \cos x)} \, dx = \frac{x^2}{2} \bigg| \limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} + \int\limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} {\cos x} \, dx[/tex][Right Integral] Trigonometric Integration: [tex]\displaystyle \int\limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} {(x + \cos x)} \, dx = \frac{x^2}{2} \bigg| \limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} + \sin x \bigg| \limits^{\frac{\pi}{2}}_{\frac{\pi}{3}}[/tex]Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^{\frac{\pi}{2}}_{\frac{\pi}{3}} {(x + \cos x)} \, dx = \frac{5 \pi ^2}{72} + \bigg( 1 - \frac{\sqrt{3}}{2} \bigg)[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Given sin x = a/2 and tanx< 0 find cos x
Answer:
cosθ = ( √4 - a² ) ÷ 2
Explanation:
sinθ = a/2
according to sincostan rule:
sinθ = opposite/ hypotenuse
cosθ = adjacent/ hypotenuse
so here opposite is a and hypotenuse is 2
adjacent² + opposite² = hypotenuse²
adjacent² + a² = 2²
adjacent = √4 - a²
we found our adjacent.
so cosθ = adjacent/ hypotenuse
= ( √4 - a² ) / 2
so cosθ = [tex]\frac{ \sqrt{4 - a^{2}} }{2}[/tex]
What is the slope of the graph of x - 2y = 8?
A. 0
B. 1/2
C. 2
D. -1/2
Answer:
1/2
Step-by-step explanation:
-2y= 8-X
y= -4+X/2
y= X/2-4
recall that: y= mx+c
in the equation y= x/2+C
m=1/2
where m is your slope
please help!!!!!! will mark brainlist
Answer:
TW/UV=WX/UX
Two triangles are similar when all of their angles are equal & Ratio of side to side is equal when two triangles are similar.
Given that a=4, b=4 and c=-2 work out b(squared) -2ac
Answer:
32
Step-by-step explanation:
substitute the given values of a, b and c into the expression:
b² - 2ac = 4² - (2 x 4 x -2)
= 16 - (-16)
= 16 + 16
= 32
PLEASE HELP!! WILL GIVE BRAINLIEST IF YOU ANSWER SOON!!!
Answer:
b
Step-by-step explanation:
math
Select all the expressions that are equal to 0.09 x 0.4
1. 9/100 × 4/10
2. 4/100 × 9/100
3. 9/10 × 4/10
4. 4/10 × 9/100
5. 40/100 × 9/100
Answer:
option no.1
option no. 4
option no. 5
hope it helped u
Answer:
option 1
option 4
option 5
What is the surface area of the cylinder with height 6 ft and radius 6 ft? Round your
answer to the nearest thousandth.
The surface area of this cylinder to the nearest thousandth is equal to 452.448 square feet.
Given the following data:
Height of cylinder = 6 ft.Radius of cylinder = 6 ft.To calculate the surface area of this cylinder to the nearest thousandth:
How to calculate surface area.Mathematically, the surface area (SA) of a cylinder is given by this formula:
[tex]SA = 2\pi rh + 2\pi r^2[/tex]
Where:
h is the height.r is the radius.Substituting the given parameters into the formula, we have;
[tex]SA = 2 \times 3.142 \times 6 \times 6 + 2 \times 3.142 \times 6^2\\\\SA = 226.224 + 226.224[/tex]
SA = 452.448 square feet.
Read more on surface area here: https://brainly.com/question/21367171
Your current exam mean is 95. If you receive a 95 on the next exam, your mean ______. a. will remain the same b. will increase c. will decrease d. cannot be determined
Answer:
will remain the same
Step-by-step explanation:
Examples:
Your current exam mean is 97.2. If you receive a 99 on the next exam, this will have the effect of: increasing your mean
Your current exam mean is 93.2. If you receive a 87 on the next exam, this will have the effect of: decreasing your mean
Therefore, Your current exam mean is 95. If you receive a 95 on the next exam,this will have the effect of: Will remain the same
Unit 11 volume & surface area homework 4 area of regular figures
The area of a shape is the amount of space occupied by the shape
The area of the triangle is 216 square centimeters
How to calculate the surface areaThe dimension of the triangle is given as:
Base = 27 cm
Height = 16 cm
The area of the triangle is then calculated as:
Area = 0.5 * Base * Height
So, we have:
Area = 0.5 * 27 cm * 16 cm
Evaluate the product
Area = 216 square cm
Hence, the area of the triangle is 216 square centimeters
Read more about surface areas at:
https://brainly.com/question/24571594
James has 9 liters of milk. If each glass holds one-third of a liter, how
many glasses can he fill?
Answer:
9\1/3 is equal to 27
Step-by-step explanation:
if u divide the nine by 1/3 you get 27therefore he can fill 27 cups
which expression is equivalent to 4/6 of 36 ?
Answer:
First, find the answer for 36 ÷ 4. Which is 9.
Now calculate each expression until you get the answer of 9.
4 ÷ 36 = 4 * 1/36 = 4/36 = 1/9
36 ÷ 1/4 = 36 * 4 = 144
1/36 * 1/4 = 1/144
36 * 1/4 = 36/4 = 9
So, the last option is the answer. D. 36 * 1/4.
Answer:
35 1/3 I believe
Step-by-step explanation:
36 divided by 4/6 and you 35 1/3
Please help me with this question :(
Answer:
∠1 and ∠3 as well as ∠5 and ∠7 are corresponding
∠2 and ∠7 are alternate
Step-by-step explanation:
The first two terms in an arithmetic progression are 57 and 46. The last term is -207. Find the sum of all the terms in this progression.
Answer:
-1875
Step-by-step explanation:
An arithmetic sequence has a common difference as a sequence. Here the common differnece is -11.
So our sequence so far looks like,
(57,46,35,24....). We know the last term of the sequence is -207 and we need to find the nth term of that series so we use arithmetic sequence
[tex]a _{1} + (n - 1)d [/tex]
where a1 is the inital value,
d is the common differnece and n is the nth term.
We need to find the nth term so
[tex]57 + (n - 1)( - 11) = - 207[/tex]
[tex](n - 1)( - 11) = - 264[/tex]
[tex]n - 1 = 24[/tex]
[tex]n = 25[/tex]
So the 25th term of a arithmetic sequence is last term, now we can use the sum of arithmetic sequence
which is
[tex] \frac{a _{1} + a _{n} }{2} n[/tex]
[tex] \frac{57 + ( - 207)}{2} (25) = [/tex]
[tex] \frac{ - 150}{2} (25)[/tex]
[tex] - 75(25) = - 1875[/tex]
Answer:
-1875
Step-by-step explanation:
57 , 46 , ......... -207
[tex]First \ term = \ a_{1} = 57\\[/tex]
common difference = d = second term - first term = 46 - 57 = -11
[tex]n^{th} \ term = -207\\\\a + (n-1)*d=t_{n}[/tex]
57 + (n-1)* (-11) = -207
57 - 11n + 11 = -207
-11n + 68 = -207
-11n = -207 - 68
-11n = -275
n = -275/-11
n = 25
[tex]S_{n}=\dfrac{n}{2}(a_{1}+l)\\\\\\S_{25}=\dfrac{25}{2}*(57 + (-207) )\\\\\\ =\dfrac{25}{2}* (-150)\\\\\\= 25 *(-75)\\\\= -1875[/tex]
What is the slope of the line graphed above?
Answer: -2/5
Step-by-step explanation: down 2 right 5
FIND X PLS HELP MEE plss
The solution to the system is (6,2).
Select all the equations that could be the other equation in the system.
A y=−3x
B y=−3/2x+6y
C y=−1/6x+3y
D y=2/3x−1y
E y=1/2x−1y
F y=4x -2
What two numbers multiply to get -40 and add up to get -3
Answer:
5 and -8
Step-by-step explanation:
First, list the set of pairs of numbers that multiply to give 40 (so "factors" of 40):
1 40
2 20
4 10
5 8
Now look at the pairs to see which has a difference of 3.
1 and 40 has a difference of 39
2 and 20 has a difference of 18
4 and 10 has a difference of 6
5 and 8 has a difference of 3
Now all we need to do is determine whether 5 or 8 will be negative (if they are both negative, the product will be positive, so only one needs to be negative to have a product of -40).
As we need a final result of -3, the two numbers will be: 5 and -8 (as 5 + - 8 = -3)
Answer:
5 and -8
Step-by-step explanation:
First I listed all the factors of 40 : 1, 2, 4, 5, 8, 10, 20 and 40.
Then out of those, I just had to find a pair with a difference of 3.
Or in other words, when I subtracted one from the other I either got 3 or -3.
The only pair that worked out that way when subtracted was 5 and 8.
However, if we multiply 5 and 8 we get 40, not -40, so something was amiss. When we add them up we have to get -3, and that only worked out if it was -8 and 5, since -8 + 5 = -3.
Therefore, the two numbers are -8 and 5
Hope this helps, please mark brainliest if possible :)
Simplify (3y^6)^5/(y^3)^5
Answer: 245y^15
Step-by-step explanation:
Simplify by combining the like terms: 4(c + 9) - 5 + 6c + 2c
[tex]12c + 31\\12c - 4\\12c + 4[/tex]
Answer:
12c+31
Step-by-step explanation:
[tex]4(c+9)=4c+36\\[/tex](4x everything in parenthesis)
[tex]4c+6c+2c=12c[/tex]
[tex]36-5=31[/tex]
[tex]12c+31[/tex]
Somebody help Janele! XD
quartz gym....interesting, janele
Answer:
D
Step-by-step explanation:
So when making these equations, there's always going to be an initial value and then a variable
In this case, x represents the unknown cost for each class that Janele took at the rock climbing gym. She took 6 classes, so that's represented by 6x
50 is the initial value. The initial value is a value that is constant, or stays the same. It doesn't change based on variables like how many classes she took.
The total cost of everything was 92 dollars
So then ur equation would be
6x + 50 = 92
Because both the initial cost of 50 dollars and the cost of the classes equal to 92
lol Janele and the quartz gym, some of these math problems really do be interesting. like jim and his 100 watermelons from costco
a strand of christmas lights measures 5/8 yards long. jake needs to outline a square with sides 1/5 yards long. does he have enough to outline the square?
Answer:
No, it's not long enough
Step-by-step explanation:
The perimeter of the square is 4/5. P=4s where s is the side length. 4/5 is larger than 5/8, so there will not be enough lights to cover the whole perimeter.
Mr. Jenkins recorded the amount of weight he lost in six months.
If Mr. Jenkins wanted to brag about losing the most weight, which measure of central tendency would he use?
Answer: Mr. Jenkins would use 'mean'.
Step-by-step explanation:
Rather than use either median or mode, he would use mean. Mean is a statistical average of numbers. It would be best to brag about the total weight that he has lost rather than using the half-way point or the most frequent appearing number in the data.
I will mark brainliest if someone can help me with this geometry question
Answer:
B
Step-by-step explanation:
Since the triangle has 2 equal base angles (45 degrees) and 1 angle is 90 degrees, the triangle is an isosceles right triangle.
We let a be the length of one side of the right angle, so the length of the other side is also a. Applying the Pythagorean theorem we have a^2 + a^2 =14^2 => a=[tex]7\sqrt{2}[/tex]
We have the area of an equilateral triangle 1/2 the product of the lengths of the 2 sides of the right angle. S=1/2*[tex]7\sqrt{2} * 7\sqrt{2}[/tex]=49
HELP!! will give brainliest
The point P with coordinates (-13,9) is reflected in the line y = -x. Without an accurate drawing as a sketch, write down the coordinates of the image of P.
Transformation involves changing the coordinates of a point
The coordinates of the image of P is (9,13)
How to determine the coordinates of the image of PThe coordinate of P is given as:
P = (-13,9)
The rule of reflecting the point over the line y = -x is represented as:
[tex](x,y) \to (y,-x)[/tex]
So, we have:
[tex](-13,9) \to (9,13)[/tex]
This means that:
[tex]P' = (9,13)[/tex]
Hence, the coordinates of the image of P is (9,13)
Read more about transformation at:
https://brainly.com/question/4057530
11. Solve the equation n/10 + 7 = 10
Answer:
n = 30
Step-by-step explanation:
Step 1: Subtract 7 from both sides.
[tex]\frac{n}{10} + 7 - 7 = 10 - 7[/tex] [tex]\frac{n}{10} = 3[/tex]Step 2: Multiply both sides by 10.
[tex]\frac{n}{10} * 10 = 3 * 10[/tex] [tex]n = 30[/tex]Step 3: Check if solution is correct.
[tex]\frac{30}{10} + 7 = 10[/tex] [tex]3 + 7 = 10[/tex] [tex]10 = 10[/tex]Therefore, n = 30.
f(x)=3x-5 find (2)
f(2)=
Answer:
1
Step-by-step explanation:
I think the answer is one
