What is a rule for the total cost of the tickets ? Give the rule in words and as a algebraic expression
Answers
ur equation would be : y = 12x + 150....where x is the number of students and y is the total cost...but that is an equation, and u want an expression...so I guess the expression would be 12x + 150
the cost of each ticket (12) multiplied by the number of students (x), added to 150 will give u the total cost
so theh rule is 12s+150 where s is the number of students
Related Questions
I don't understand this and would appreciate an explanation as well :)
Solve for the variable in the equations below.
Round your answers to the nearest hundredth.
Do not round any intermediate computations.
e^x = 6
4^(y+3) = 3
[tex]e^x = 6[/tex]
[tex]4^y^+^3 = 3 [/tex]
Answers
[tex]e^{x}=6[/tex]
and
[tex]4^{y+3}=3[/tex]
First equation.
Take natural log of each side.
[tex]ln(e^{x})=ln(6)\\xln(e)=ln(6)\\ x=ln(6)=1.7918[/tex]
Note that ln(e) = 1 by definition.
Answer: x = 1.79 (nearest hundredth)
Second equation.
Take natural log of each side.
[tex]ln(4^{y+3})=ln(3)\\ (y+3)ln(4)=ln(3)\\ y+3= \frac{ln(3)}{ln(4)} =0.7925\\y=0.7925-3=-2.2075[/tex]
Answer: y = -2.21 (nearest hundredth)
I need to find the answer to these questions in about 10 minutes or I'm screwed. please help me out.
Answers
For the second figure, the construction of the above figure in the circle represents how to find the intersection of the perpendicular bisectors of triangle ABC.
For the third figure, the statement that is demonstrated in the in line P intersecting line m perpendicularly is the set of points equidistant from the endpoints of a line segment is the perpendicular bisector of the segment.
Determine the standard variation of the data below. (1, 2, 3, 4, 5)
Answers
μ = (1 + 2 + 3 + 4 + 5) / 5 = 3
Then, we calculate for the summation of the squares of differences of these numbers from the mean, S
S = (1 - 3)² + (2 - 3)² + (3 - 3)² + (4 - 3)² + (5 - 3)²
S = 10
Divide this summation by the number of items and take the square root of the result to get the standard deviation.
SD = sqrt (10 / 5) = sqrt 2
SD = 1.41
Thus, the standard deviation of the given is equal to 1.41.
Answer:
So basically sqrt of 2...
Step-by-step explanation:
A farmer had 17 sheep. all but 9 died. how many live sheep were left
Answers
Three times the difference of a number x and seven is twenty-three minus the sum of three times a number x and two. what is the value of x?
Answers
3x - 21 = 23 - 3x - 2 =
3x - 21 = -3x + 21
3x + 3x = 21 + 21
6x = 42
x = 42/6
x = 7 <==
The required value of x is 7.
What are linear equation?A linear equation only has one or two variables. No variables in a linear equation is raised to power greater than 1 or used as denominator of a fraction.
Now the given statement is,
Three times the difference of a number x and seven is twenty-three minus the sum of three times a number x and two.
So converting them into numerical form,
the difference of a number x and seven = x - 7
∴ Three times the difference of a number x and seven = 3(x - 7)
Similarly,
the sum of three times a number x and two = 3x + 2
∴ Twenty-three minus the sum of three times a number x = 23 - (3x + 2)
Therefore, the required equation is,
3(x - 7) = 23 - (3x + 2)
Expanding the brackets we get,
3x - 21 = 23 - 3x - 2
or, 3x - 21 = 21 - 3x
Taking alike terms together,
3x + 3x = 21 + 21
or, 6x = 42
Dividing both side by 6 we get,
x = 7
which is the required value of x.
Thus, The required value of x is 7.
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Martin is asked to find the probability of getting one head and three tails on for coin tosses this is a simple event
Answers
HTTT
THTT
TTHT
TTTH
Assuming the coin is a fair coin, we have:
Probability of tossing head is 0.5
Probability of tossing tail is 0.5
Probability of tossing the coin four times for each outcome combination listed above is
HTTT = 0.5×0.5×0.5×0.5 = 0.0625
THTT = 0.5×0.5×0.5×0.5 = 0.0625
TTHT = 0.5×0.5×0.5×0.5 = 0.0625
TTTH = 0.5×0.5×0.5×0.5 = 0.0625
Hence, probability of getting three tails and one head from 4 tossing is
4×0.0625 = 0.25
Answer: False
Martin is asked to find the probability of getting one head and three tails on for coin tosses this is a simple event.
A. True
B. False
What is 5 plus 5 minus 5 divided by 5 and then multiplied by 5?
Answers
So you have 5+5-5/5(5)
We will divide first:
5+5-1(5)
Then multiply:
5+5-5
Then add and subtract from left to right:
10-5=5
Hope that helps.
Answer:
45Step-by-step explanation:
[tex](5+5-5:5)\cdot5\\\\\text{Use PEMDAS}\\\\\text{P Parentheses first}\\\text{E Exponents}\\\text{MD Multiplication and Division (left-to-right)}\\\text{AS Addition and Subtraction (left-to-right)}\\\\=(5+5-1)\cdot5\\\\=(10-1)\cdot5\\\\=9\cdot5\\\\=45[/tex]
In which case would it be best to use the “Factoring Method” to solve the trinomial equation?
x^2 + 4x = -5
4.3x^2 + 2.4x - 3 = 0
x^2 - 4x + 3 = 0
Answers
In this case, (x-3)(x-1). -1*-3=3 and -1+-3=-4
A new machine can make 10,000 aluminum cans three times faster than an older machine. with both machines working, 10,000 cans can be made in 9 hours. how long would it take the new machine, working alone, to make the 10,000 cans?
Answers
Since the new machine is three times faster, it takes (12 hours) / 3 = 4 hours for the new machine to make 10,000 cans alone.
Let's denote the time it takes the older machine to make 10,000 cans as "t" hours.
The new machine can make 10,000 cans three times faster than the older machine, which means it takes "t/3" hours for the new machine to make 10,000 cans.
When both machines are working together, they can make 10,000 cans in 9 hours.
Now, we can set up an equation based on the work rates of the two machines:
Work rate of the older machine + Work rate of the new machine = Combined work rate
The work rate is the amount of work (number of cans made) per unit of time (hours).
For the older machine:
Work rate of the older machine = 10,000 cans / t hours
For the new machine:
Work rate of the new machine = 10,000 cans / (t/3) hours
Combined work rate when both machines work together:
Combined work rate = 10,000 cans / 9 hours
Now, the equation becomes:
10,000 cans / t hours + 10,000 cans / (t/3) hours = 10,000 cans / 9 hours
To solve for "t," we can start by finding a common denominator for the fractions on the left side of the equation:
t/3 is the same as (1/3)t. So the equation becomes:
10,000 cans / t hours + 10,000 cans / (1/3)t hours = 10,000 cans / 9 hours
Now, to combine the fractions, we find the common denominator, which is 3t:
(3t * 10,000 cans) / (3t * t hours) + (t * 10,000 cans) / (3t * t hours) = 10,000 cans / 9 hours
(30,000t + 10,000t) / (3t^2 hours) = 10,000 cans / 9 hours
Combine the terms on the left side of the equation:
40,000t / (3t^2 hours) = 10,000 cans / 9 hours
Now, cross-multiply to solve for "t":
40,000t * 9 hours = 10,000 cans * 3t^2 hours
360,000t hours = 30,000t^2 hours
Now, rearrange the equation:
30,000t^2 - 360,000t hours = 0
Divide by 30,000t to simplify the equation:
t - 12 = 0
Now, solve for "t":
t = 12 hours
Therefore, it takes the older machine 12 hours to make 10,000 cans.
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5v + 7f =28.70 if f is 2.85
Answers
5v+7(2.85)=28.70
5v+19.95 = 28.70
5v = 8.75
v = 1.75
First, let's write the problem.
[tex]5v+7\left(2.85\right)=28.7[/tex]
Multiply [tex]7[/tex] with [tex]2.85[/tex].
[tex]5v+19.95=28.7[/tex]
Subtract [tex]19.95[/tex] from both sides.
[tex]5v+19.95-19.95=28.7-19.95[/tex]
[tex]5v=8.75[/tex]
Divide both sides by [tex]5[/tex].
[tex]\frac{5v}{5}=\frac{8.75}{5}[/tex]
[tex]v=1.75[/tex]
Let me know if you have any questions regarding this problem!
Thanks!
-TetraFish
In triangle PQR, C is the centroid.
A. If CY = 10, find PC and PY
B. If QC = 10, find ZC and ZQ
C. If PX = 20, find PQ
Answers
Because point C is the centroid of the triangle, therefore:
Segments PZ = ZR; RY = YQ; QX = XP
A.
If CY = 10, then
PC = 2*CY = 20
PY = PC + CY = 20 + 10 = 30
Answers:
PC = 20
PY = 30
B.
If QC = 10, then
ZC = QC/2 = 5
ZQ = ZC + QC = 5 + 10 = 15
Answers:
ZC = 5
ZQ = 15
C.
If PX = 20
because the median RX bisects side PQ, therefore PX = QX = 20
PQ = PX + QX = 40
Answer:
PQ = 40
What is the missing step in this proof?
Answers
Statement: Angle 1 and angle 4 are congruent, and angle 3 and angle 5 are congruent.
Reason: Alternate Interior Angles Theorem
Hope this helps!
The missing step in the proof is;
Statement: ∠1 ≅ ∠4 and ∠3 ≅ ∠5Reason: Alternate interior angle theorem.The correct answer choice is option C.
What is alternate interior angles theorem?Alternate angle theorem states that when two parallel lines are cut by a transversal, the resulting alternate interior or exterior angles are congruent.
It is used to prove that alternate interior angles are equal if two parallel lines are cut by a transversal,
Hence, angle 1 is congruent to angle 4 and angle 3 is congruent to angle 5.
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Using the Law of Cosines, in triangle DEF, if e=18yd, d=10yd, f=22yd, find measurement of angle D
Answers
[tex]\bf \textit{Law of Cosines}\\ \quad \\ c^2 = {{ a}}^2+{{ b}}^2-(2{{ a}}{{ b}})cos(C)\implies c = \sqrt{{{ a}}^2+{{ b}}^2-(2{{ a}}{{ b}})cos(C)} \\\\\\ \cfrac{{{ a}}^2+{{ b}}^2-c^2}{2{{ a}}{{ b}}}=cos(C)\implies cos^{-1}\left(\cfrac{{{ a}}^2+{{ b}}^2-c^2}{2{{ a}}{{ b}}}\right)=\measuredangle C\\\\ -------------------------------\\\\ \begin{cases} d=10\\ e=18\\ f=22 \end{cases}\implies cos^{-1}\left(\cfrac{{{ 18}}^2+{{ 22}}^2-10^2}{2(18)(22)}\right)=\measuredangle D[/tex]
[tex]\bf \implies cos^{-1}\left(0.893\overline{93}\right)=\measuredangle D\implies 26.63^o\approx \measuredangle D[/tex]
Julio paid 1.3 times his normal hourly rate for each he works over 31 hours in a week. Last week he worked 35 hours and earned $448.88. What is julios normal hourly rate ?
Answers
All the time worked past 31 hours gets paid 1.3 times.
He worked 4 hours at such a rate.
31+4(1.3)
31+5.2
=36.2
Paid as if he worked 36.2 at a normal rate.
To find his normal wage, divide 448.88 by 36.2
448.88/36.2
=12.40
His normal wage is $12.40.
To check:
12.40*31=384.40
12.40*1.3=16.12
16.12*4=64.48
384.40+64.48
=$448.88
Hope this helps.
-Benjamin
Let his hourly rate is x
then:
31x + (35-31)*1.3x = 448.88
solve for x:
31 x + 5.2x = 448.88
36.2 x =448.88
x = 12.4$
not fair hourly rate by the way ;)
a triangle has two sides of the lengths 8 and 10 what value could the length of the third side be
Answers
Pythagorean theorem proof: 6^2+8^2=10^2, or 36+64=100
Which rate is the lowest price?
$6.30 for 9
$5.50 for 5
$4.20 for 7
$0.80 each
Answers
This problem can be solved by dividing the pay by the number of items.
$6.30 / 9 = $0.70
$5.50 / 5 = $1.10
$4.20 / 7 = $0.60
$0.80 / 1 = $0.80
This shows that for the third option, $4.20 for 7, the rate per item is the lowest.
In how many ways can 2 singers be selected from 4 who came to an audition?
A. 6
B. 2
C. 12
D. 4
In a batch of 280 water purifiers, 12 were found to be defective. What is the probability that a water purifier chosen at random will be defective? Write the probability as a percent. Round to the nearest tenth of a percent if necessary.
A. 4.3%
B. 5.6%
C. 95.7%
D. 71.8%
Answers
Second part
12 * 100
---------- = 4.3 %
280
Answer: A. 6
A. 4.3%
Step-by-step explanation:
The total number of singers = 4
To choose singers = 2
The number of ways to choose 2 singers from 4= [tex]^4C_2=\frac{4!}{2!(4-2)!}=3\times2=6[/tex]
Hence, A is the right option.
The total number of water purifiers T= 280
The number of defective purifiers D= 12
The probability that a water purifier chosen at random will be defective (in percent)=[tex]\frac{\text{T}}{\text{D}}\times100[/tex]
[tex]=\frac{12}{280}\times100\\=0.042857\times100\\=4.2857\%\approx4.3\%[/tex]
Hence, A is the right option.
State the Midpoint formula?
How are the midpoint formula and the Distance formula alike? How are they different?
Give a real-world example that could be addressed using the distance formula.
Give a real-world example that could be addressed using the midpoint formula.
Answers
Mid-point formula is given by: [tex][ \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}] [/tex]
The distance formula is given by: [tex] \sqrt{(x_1-x_2)^2+(y_1-y_2)^2} [/tex]
The two formula are alike because they both need the information of two coordinate points
They are different because the mid point formula is adding up then divide by two, whereas the distance formula is subtracting then square the answer.
--------------------------------------------------------------------------------------------------------------
Real life problem involving distance formula:
Plane A is spotted on a radar with cartesian coordinate (450, 640).
Plane B is spotted on the same radar with cartesian coordinate (350, 540)
Work out the distance between plane A and plane B.
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Real life problem involving mid point formula
Ms. Holland arranges a treasure hunt for a group of scouts. She marks two points, C and D, with cartesian coordinate (-5, 6) and (7, 10) respectively. The clue is that the treasure is buried in the middle point between C and D. Work out the coordinate where the treasure is buried.
For a fixed amount of a gas at a constant temperature, the volume of the gas is inversely proportional to its pressure. At a pressure of 30 pounds per square inch (psi), a gas has a volume of 600 in.3. Which function can be used to model the volume of the gas y, in cubic inches, when the pressure is x psi?
Answers
we know that
A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]
Let
x-------> the pressure in PSI
y------> the volume of the gas in cubic inches
In this problem we have the point [tex](30,600)[/tex]
so
[tex]x=30\ psi\\y=600\ in^{3}[/tex]
Find the constant k
[tex]y*x=k[/tex]
substitute the values of x and y
[tex]600*30=k[/tex]
[tex]k=18,000\ lb*in[/tex]
the equation is
[tex]y=18,000/x[/tex]
therefore
the answer is
[tex]y=18,000/x[/tex]
Answer:
[tex]y=\frac{18000}{x}[/tex]
Step-by-step explanation:
Let the volume of gas be y
Let the pressure be x
Since we are given that the volume of the gas is inversely proportional to its pressure.
⇒[tex]y \propto \frac{1}{x}[/tex]
Let the proportionality be k
So, [tex]y=\frac{k}{x}[/tex] ---A
Now we are given that At a pressure of 30 pounds per square inch (psi), a gas has a volume of 600 cubic inches
So, substitute x = 30
y = 600
[tex]600=\frac{k}{30}[/tex]
[tex]600 \times 30=k[/tex]
[tex]18000 =k[/tex]
Substitute the value of k in A
So, [tex]y=\frac{18000}{x}[/tex]
Hence function can be used to model the volume of the gas y, in cubic inches, when the pressure is x psi is [tex]y=\frac{18000}{x}[/tex]
A school director must randomly select 6 teachers to participate in a training session. There are 34 teachers at the school. In how many different ways can these teachers be selected, if the order of selection does not matter?
Answers
where [tex]C(n, r)= \frac{n!}{r!(n-r!)} [/tex]
n! meaning 1*2*3*....*(n-1)*n
According to this, the selection of 6 teachers out of 34, can be carried out in C(34, 6) many different ways.
[tex]C(34, 6)= \frac{34!}{6!(34-6!)}=\frac{34!}{6!(28!)}= \frac{34*33*32*31*30*29*28!}{6!28!}= \frac{34*33*32*31*30*29}{6!}[/tex]
[tex]=\frac{34*33*32*31*30*29}{6*5*4*3*2*1}= 34*11*4*31*29=1,344,904[/tex]
Solve the equation: 2.6 = -0.2t
Answers
2.6 / -0.2 = t
-13 = t <==
T=2.6/-0.2=-13
T= -13
Hope this helps!
Identify a semicircle that contains C.
A.ABC
B.AC
C.CB
D. ACB
Answers
Answer: The correct option is (D). ACB.
Step-by-step explanation: We are given to identify a semi-circle that contains the point 'C'.
As shown in the figure, AB is the diameter of the circle with center 'O'.
So, there are two congruent semi-circles made by the diameter AB.
The point 'C' lies on the upper semi-circle made by the diameter AB.
Since the upper semi-circle contains the point 'C', so it is named as the semi-circle ACB.
Thus, the semi-circle ACB contains the point 'C'.
Option (D) is correct.
Find the length of the diameter of a sphere with a surface area of 452.39^2 ft.
Answers
surface area = 4*pi*r^2
using 3.14 for pi
452.39 = 4*3.14*r^2=
452.39=12.56* r^2
r^2 = 452.39/12.56 = 36.0
sqrt(36) = 6= r
diameter = 2r = 6*2= 12
diameter = 12 feet
A store's cost for a stereo was $27. The markup was 75%. A customer purchased it on sale at 40% off the markup price. What was the purchase price of the stereo
Answers
if we take 27 to be the 100%, what's 175% of that?
[tex]\bf \begin{array}{ccllll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 27&100\\ x&175 \end{array}\implies \cfrac{27}{x}=\cfrac{100}{175}\implies \cfrac{27\cdot 175}{100}=x\implies \boxed{47.25=x}[/tex]
alrite, then a customer showed up and found it on sale, 40% off that price, so if you take out 40% from the 100%, the price the customer found it at is the 60%, 100-40, of the current price of 47.25
so, if 47.25 is the 100%, what's 60% of that?
[tex]\bf \begin{array}{ccllll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 47.25&100\\ x&60 \end{array}\implies \cfrac{47.25}{x}=\cfrac{100}{60}[/tex]
solve for "x".
Which is a sum of cubes? a3 + 18 a6 + 9 a9 + 16 a12 + 8
a3 + 18
a6 + 9
a9 + 16
a12 + 8
Answers
Answer: [tex]a^{12}+8[/tex]
Step-by-step explanation:
let's check all the expressions
1. [tex]a^3+18[/tex]
here 18 is not a perfect cube.
2. [tex]a^6+9[/tex]
here 9 is not a perfect cube.
3.[tex]a^9+16[/tex]
here 16 is not a perfect cube.
4.[tex]a^{12}+8[/tex]
here 8 is a perfect cube, thus we can write above expression by using laws of exponents as
[tex](a^4)^3+2^3[/tex]
Thus, [tex]a^{12}+8[/tex] is a sum of cubes.
How do you get rid of an exponent on a variable?
Answers
To get rid of an exponent on a variable, apply the inverse operation of the exponent such as division or root operations.
Explanation:To get rid of an exponent on a variable, you need to apply the inverse operation of the exponent. If the exponent is multiplication, you use division, and if the exponent is an exponentiation, you use a root operation. For example, to get rid of a squared variable, you take the square root of the variable. If you have a variable raised to the third power, you take the cube root of the variable.
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Solve the equation: h/9 = 7. A. h = 1 2/7 B. h = 63 C. h = –63 D. h = 7/9
Answers
The answer is: B. h= 63
HELPPP Plzzzzzzzzzz ASAP
Use Addition of Composite Figures to find the total shaded regions.
1) Find the shaded area. Round your answer to the nearest tenth, if necessary.
Answers
The sum of the digits of a certain number is 12. When you reverse its digits you decrease the number by 36. Find the number
Answers
x+y=12
x*y =36
8+4=12, so make the digits 84, reverse to make it 48
84-48=36
the numbers are 8 & 4
A wire is first bent into the shape of a rectangle with width
4in and length 14in. Then the wire is unbent and reshaped into a square. What is the length of a side of the square?
Answers
Area of a rectangle=L*W= 14*4=56
Then divide that by 4 since a square has 4 equal sides
56/4=14
The length of a side of a square is 14 in