Answer:
170 children
74 students
85 adults
Step-by-step explanation:
Given
Let:
[tex]C = Children; S = Students; A = Adults[/tex]
For the capacity, we have:
[tex]C + S + A = 329[/tex]
For the tickets sold, we have:
[tex]5C + 7S + 12A = 2388[/tex]
Half as many as adults are children implies that:
[tex]A = \frac{C}{2}[/tex]
Required
Solve for A, C and S
The equations to solve are:
[tex]C + S + A = 329[/tex] -- (1)
[tex]5C + 7S + 12A = 2388[/tex] -- (2)
[tex]A = \frac{C}{2}[/tex] -- (3)
Make C the subject in (3)
[tex]C = 2A[/tex]
Substitute [tex]C = 2A[/tex] in (1) and (2)
[tex]C + S + A = 329[/tex] -- (1)
[tex]2A + S + A = 329[/tex]
[tex]3A + S = 329[/tex]
Make S the subject
[tex]S = 329 - 3A[/tex]
[tex]5C + 7S + 12A = 2388[/tex] -- (2)
[tex]5*2A + 7S + 12A = 2388[/tex]
[tex]10A + 7S + 12A = 2388[/tex]
[tex]7S + 22A = 2388[/tex]
Substitute [tex]S = 329 - 3A[/tex]
[tex]7(329 - 3A) + 22A = 2388[/tex]
[tex]2303 - 21A + 22A = 2388[/tex]
[tex]2303 +A = 2388[/tex]
Solve for A
[tex]A = 2388 - 2303[/tex]
[tex]A = 85[/tex]
Recall that: [tex]C = 2A[/tex]
[tex]C = 2 * 85[/tex]
[tex]C = 170[/tex]
Recall that: [tex]S = 329 - 3A[/tex]
[tex]S = 329 - 3 * 85[/tex]
[tex]S = 329 - 255[/tex]
[tex]S = 74[/tex]
Hence, the result is:
[tex]C = 170[/tex]
[tex]S = 74[/tex]
[tex]A = 85[/tex]
Answer:
Down Below
Step-by-step explanation:
The answer is actually
162 children
86 students
81 adults
162x5=810
86x7=602
81x12=972
I found the original problem and the total ticket sale was $2384.
So I wrote the answers for the original problem just in case!
Ty for your time!
Which expression can be used to find the quotient of 184 and 8?
(184÷10)+(8÷2)
(160÷8)+(24÷8)
(18÷3)+(4-2)
(184÷4)+(8÷2)
????????
Factor the expression completely.
35 + 2x2 – 24
Answer:
[tex]2x^{2} +11[/tex] cannot be simplified further
Step-by-step explanation:
Tina walked her dog 12 blocks. This is twice the number of blocks she walked yesterday. How far did Tina walk her dog yesterday?
Answer: Hello, your Answer is Below ^^
Your Answer Is 6
Step-by-step explanation:
I Got the answer 6 Because 6 x 2 = 12
Tina Walked 12 blocks and Half of 12 Is 6
Hope this helps you!
Have a great Day!
~Rainbow~
Answer:
the correct answer is 6
Step-by-step explanation:
since twice = 2 you'll need to do 12 divided by 2
which is equal to 6.
or you can simply just think what number is twice in 12.
The function f(x) is a quartic function and the zeros of f(x) are -4,-3,2 and 5. Assume the leading coefficient of f(x) is 1. Write the equation of the quartic polynomial in standard form
The equation of the quartic polynomial in standard form is,
⇒ f (x) = x⁴ - 27x² - 14x + 120
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
We have to given that;'
The function f(x) is a quartic function and the zeros of f(x) are -4,-3,2 and 5.
And, the leading coefficient of f(x) is 1.
Hence, We get;
The equation of the quartic polynomial in standard form is,
⇒ f (x) = 1 (x - (- 4)) (x - (- 3)) (x - 2) (x - 5)
⇒ f (x) = (x + 4) (x + 3) (x - 2) (x - 5)
⇒ f (x) = (x² + 7x + 12) (x² - 7x + 10)
⇒ f (x) = x⁴ - 7x³ + 10x² + 7x³ - 49x² + 70x + 12x² - 84x + 120
⇒ f (x) = x⁴ - 27x² - 14x + 120
Learn more about the quadratic equation visit:
brainly.com/question/1214333
#SPJ2
5) Abhasra invests $7,053 in a savings
account with a fixed annual interest rate of
3% compounded quarterly. What
will the account balance be after 4 years?
Answer:
After 4 years the account balance will be $ 7,948.67.
Step-by-step explanation:
Given that Abhasra invests $ 7,053 in a savings account with a fixed annual interest rate of 3% compounded quarterly, to determine what the account balance will be after 4 years, the following calculation must be performed:
7.053 x (1 + 0.03 / 4) ^ 4x4 = X
7,053 x 1.0075 ^ 16 = X
7.053 x 1.12699211 = X
7,948.67 = X
Therefore, after 4 years the account balance will be $ 7,948.67.
Question 7Partially correct answer. Your answer is partially correct. Try again.An article in Knee Surgery, Sports Traumatology, Arthroscopy (2005, Vol. 13, pp. 273-279), considered arthroscopic meniscal repair with an absorbable screw. Results showed that for tears greater than 25 millimeters, 13 of 19 repairs were successful while for shorter tears, 22 of 30 repairs were successful.(a) Is there evidence that the success rate is greater for longer tears
This question is incomplete, the complete question is;
An article in Knee Surgery, Sports Traumatology, Arthroscopy (2005, Vol. 13, pp. 273-279), considered arthroscopic meniscal repair with an absorbable screw. Results showed that for tears greater than 25 millimeters, 13 of 19 repairs were successful while for shorter tears, 22 of 30 repairs were successful.
a) Is there evidence that the success rate is greater for longer tears? Use alpha=0.05
Answer:
P-value = 0.6443
Now, since the p-value( 0.6443 ) is greater than the significance level (0.05), We fail to reject null hypothesis.
Therefore, there is no significant difference in the successive proportion ( rate ). [tex]p[/tex]₁ = [tex]p[/tex]₂
Step-by-step explanation:
Given the data in the question;
Sample of tears greater than 25;
number of successive repairs X₁ = 13
number of repair n₁ = 19
proportion of successive repairs [tex]p[/tex]₁ = 13/19 = 0.68
q₁ = 1 - [tex]p[/tex]₁ = 1 - 0.68 = 0.32
Sample of tears shorter than 25;
number of successive repairs X₂ = 22
number of repair n₂ = 30
proportion of successive repairs [tex]p[/tex]₂ = 22/30 = 0.73
q₂ = 1 - [tex]p[/tex]₂ = 1 - 0.73 = 0.27
so;
H₀ : There is no significant difference in the successive proportions; [tex]p[/tex]₁ = [tex]p[/tex]₂
Hₐ : The successive rate is greater for longer tears [tex]p[/tex]₁ >
Significance level ∝ = 0.05
Test Statistics
Z = ([tex]p[/tex]₁ -
so we substitute
Z = ( 0.68 - 0.73 / √[ (0.68 ×0.32 / 19) + ( 0.73×0.27 / 30 ) ]
Z = -0.05 / √[ 0.01802 ]
Z = -0.05 / 0.1342
Z = -0.37
P-value for the given test, p = P( Z > -0.37 )
= 1 - P( Z ≤ - 0.37 )
= 1 - 0.35569
P-value = 0.6443
Now, since the p-value( 0.6443 ) is greater than the significance level (0.05), We fail to reject null hypothesis.
Therefore, there is no significant difference in the successive proportion ( rate ). [tex]p[/tex]₁ = [tex]p[/tex]₂
what is the volume of this rectangular prism 5/4×5/3×5/2
Answer:
the answer is one!
Step-by-step explanation:
Answer:
answer: 125/24 cm3
volume= 5/3*5/2*5/4 cm3
=125/24 cm3
Please help asap!!!!
Answer:
[tex] m\widehat {MP} =46\degree [/tex]
Step-by-step explanation:
By inscribed angle theorem:
[tex] m\angle MQP=\frac{1}{2} \times \widehat {MP} [/tex]
[tex] 23\degree =\frac{1}{2} \times m\widehat {MP} [/tex]
[tex] 23\degree \times 2= m\widehat {MP} [/tex]
[tex] m\widehat {MP} =46\degree [/tex]
In the formula, l = a + (n - 1)d make d as the subject. Find d when l = 10, a = 2, n = 5.
I = a + (n - 1)d [Given formula]
To Find:-Find d when I = 10, a = 2, n = 5
Solution:-I = a + (n - 1)d [Given]
Putting the value of I = 10, a = 2, n = 5 we get,
10 = 2 + (5 - 1)d
10 = 2 + 4d
10 - 2 = 4d
8 = 4d
d = [tex] \frac{8}{4} [/tex]
d = 2
Value of d is 2. [Answer]Mr. Robert offers students piano lessons. The cost is $25 per student plus a one-time registration fee of $50. How many lessons can a particular student take if they want to pay less than $175?
Write an inequality to represent the situation.
Define your variable in the space below.
Solve the inequality to determine how many lessons the student can take. Be sure to TYPE all your computations
Answer:
20
Step-by-step explanation:
cause
Dean made a triangular wall shelf.
The sides of the triangle measure
14 inches, 8 inches and 8 inches.
Is the shelf a right triangle?
Explain.
Answer:
The shelf is not a right triangle
Step-by-step explanation:
Given
[tex]Sides = 14, 8, 8[/tex]
Required
Determine if it is a right triangle
To do this, we make use of Pythagoras theorem which implies that; the square of the longest side = the sum of the square of the two other sides.
So, we have:
[tex]14^2 = 8^2 + 8^2[/tex]
Evaluate all squares
[tex]196 = 64 + 64[/tex]
[tex]196 = 128[/tex]
The above is not true because:
[tex]196 \ne 128[/tex]
Hence, the shelf is not a right triangle
What’s the missing side length? Round to the nearest tenth please :)))
Answer:
the answer is 4.6
Step-by-step explanation:
the explanation is shown in the following attachment below...
hope this helps...
Help please I need to complete this before 12
Answer:
Look at the answers bolded below
Step-by-step explanation:
To get the reference angle, just subtract 115° from 180°
180 - 115 = 65
So the reference angle is 65°
I'm not sure how many coterminal angles you need, but to get them you could just add or subtract 360°.
For example, a positive coterminal angle could be:
115 + 360 = 475°
a negative coterminal angle could be:
115 - 360 = -245°
Hope this helped :)
1. Which color combination is the
mode for the students' votes?
A Blue/Gold
B Green/Silver
C Blue/White
D Black/Gold
As part of a study of corporate employees, the director of human resources for PNC, Inc. wants to compare the distance traveled to work by employees at its office in downtown Cincinnati with the distance for those in downtown Pittsburgh. A sample of 40 Pittsburgh employees showed they travel a mean of 370 miles per month. A sample of 35 Cincinnati employees showed they travel a mean of 380 miles per month. Do the Cincinnati employees travel the same distance to work, on average, as the Pittsburgh employees
Answer:
Both groups of Employees do not travel the same distance to work hence we will reject the Null hypothesis
Step-by-step explanation:
40 Pittsburgh employees mean travel time = 370 miles
35 Cincinnati employees mean travel time = 380 miles
Both groups of Employees do not travel the same distance to work hence we will reject the Null hypothesis
H0 : μ1 = μ2
H1 : μ1 ≠ μ2
mean = total distance / Number of employees
For Pittsburgh
370 = x / 40
x = 370 * 40 = 14,800 miles
For Cincinnati
380 = y / 35
y = 380 * 35 = 13,300 miles
Please help I don’t understand it
I need a reason for both
9514 1404 393
Answer:
23) insufficient number of corresponding sides/angles
24) insufficient number of corresponding sides/angles
Step-by-step explanation:
In general, you need at least 3 corresponding parts to show triangle congruence. At least one of those must be a side. The attachment shows the ways triangles can be declared congruent. (HL works for right triangles, because we know the right angles are congruent to each other.)
__
23) A side is shown congruent (KL ≅ GH), and we know the vertical angles at J are congruent. However, we need another angle before we can declare the ∆GHJ congruent to anything. (One more side doesn't do it, because the two sides would not be on either side of the angle at J.)
Reason: insufficient data
__
24) A side is shown congruent (MP ≅ QS), and an angle is shown congruent (∠M ≅ ∠Q). As in the previous problem, we need at least one more angle, or we need to know that MN ≅ QR before we can declare the triangles congruent.
Reason: insufficient data
Jose reads his book at an average rate of 2.5 pages every four minutes. If Jose continues to read at exactly the same rate what method could be used to determine how long it would take him to read 20 pages?
it would take him 32 minutes. You could use divisoin and multiplecation to figure it out
Simplify the following rational expression.
(HELP PLS?)
Answer:
Simplified expression: [tex]\frac{1}{y+8 }[/tex].
The value of y that makes the expression undefined is y=-8.
Step-by-step explanation:
[tex]\frac{2y^{3}}{2y^{4}+16y^{3}}[/tex]
= [tex]\frac{2y^{3}}{2y^{3}(y+8) }[/tex]
(cancel out 2y³)
=[tex]\frac{1}{y+8 }[/tex]
A rational expression is undefined when the denominator (bottom number) is zero. So, if y equalled -8, the expression would ultimately equal [tex]\frac{1}{0}[/tex], which is undefined.
Question 8 of 10 What is the median of this data set? 14, 18, 31, 34, 44, 50 AL32.5 O B. 33 C. 31.5 D. 31
Answer:
a
Step-by-step explanation:
4n -6 = 10n
Simplify.
-----------------------------------------------------------------------------------------------------------------
Answer: n = -1
-----------------------------------------------------------------------------------------------------------------
add 6 to both sides of the equation.
4n − 6 = 10n
4n − 6 + 6 = 10n + 6
-----------------------------------------------------------------------------------------------------------------
simplify.
(add the numbers)
4n − 6 + 6 = 10n + 6
4n = 10n + 6
4n = 10n + 6
-----------------------------------------------------------------------------------------------------------------
subtract 10n from both sides.
4n − 10n = 10n + 6 − 10n
-----------------------------------------------------------------------------------------------------------------
simplify. (again)
(combine like terms) (combine like terms)
4n − 10n = 10n + 6 − 10n −6n = 10n + 6 − 10n
−6n = 6
-----------------------------------------------------------------------------------------------------------------
divide both sides by the same term.
−6n/−6 = 6/-6
n = 6/−6n = 6/−6
-----------------------------------------------------------------------------------------------------------------
simplify. (again)
(cancel terms that are in both the numerator and denominator)
n = 6/−6
(divide the numbers)
n = 6/−6
n = 1
-----------------------------------------------------------------------------------------------------------------
Answer:
n= -1
Step-by-step explanation:
what value of x will make the faction equivent 3/5=x/36
Answer:
x = 21.6
Step-by-step explanation:
Solution by Cross Multiplication
For the equation
35=x36
The cross product is
3×36=5×x
Solving for x
x=3×365
and reducing
x=21.6
Solution by Proportion
Since the equation is an equality
If
36 ÷ 5 = 7.2
Then it is true that
x ÷ 3 = 7.2
Solving for x
x = 3 × 7.2
x = 21.6
Bailey makes a conjecture that the product of two odd integers is always an odd integer. Which choice is the best proof of her conjecture
Answer:
D.
Step-by-step explanation:
Let (2a+1) be an odd number, and let (2b+1) be another odd number. The product 2(2ab+a+b)+1 is a multiple of 2 plus 1, which is an odd number.
Find the area of the complex figure.
Answer:
1,863
Step-by-step explanation:
f(x) = 36x, find f(3/2)
36
72
216
64
Answer:
f(5) = 6(5-2) = 18
Step-by-step explanation:
hope this help ~~~~~~~~------~~~~~~~~
is X greater than less than or equal to 106 degrees
Answer:
Less
Step-by-step explanation:
What is the area of this figure?
Answer:
m
Step-by-step explanation:
Sarah had a sheet of paper that was 3 inches long and 7 inches wide. What is the perimeter of the paper
Answer: 20
Step-by-step explanation:
(3+7)*2 = 20
Answer:
20 square inches
Step-by-step explanation:
KETO-SNACKS Tenlos a la mano para
Answer:
Here's 21 yummy keto snacks:
https://www.healthline.com/nutrition/best-keto-snacks
Hope u love em <3
Step-by-step explanation:
Which of the following shows the extraneous solution to the logarithmic equation log7 (3x ^ 3 + 7) - 100 + (x) = 27
Answer: X=-4
Step-by-step explanation:
Should be B on Edge.
Answer: X = -4
Step-by-step explanation:
ILL GIVE THE BRAINLIEST pls help me with this question EVERYTHING IS IN THE PICTURE PLS HELP DUE TODAY IF YOU PUT A WRONG ANSWER ILL REPORT YOU FASTER THAN ASSIGMENT IS DUE
Answer: the correct answer should be 160 but you said that didnt work so try 480
Step-by-step explanation:
I just did base times Hight 8*10 which is 80*6=480
hoped this helps:))
Answer:
80
Step-by-step explanation:
V= Bh/3
Area of base= (L × W) ÷2
(8×6)÷2 = 24
Multiply by height
24×10=240
Divide by 3 (since its a pyramid therefore has 3 sides)
240/3=80
80 is your answer