Cost of 1 adult ticket is $ 7 and cost of 1 student ticket is $ 3
Solution:
Let "a" be the cost of 1 adult ticket
Let "s" be the cost of 1 student ticket
Given that,
4 adult and 10 student tickets cost 58$ overall on the first day
So we can frame a equation as:
4 adult ticket x cost of 1 adult ticket + 10 student ticket x cost of 1 student ticket = $ 58
[tex]4 \times a + 10 \times s = 58[/tex]
4a + 10s = 58 ------ eqn 1
On the second 5 adult and 1 student cost 38$ overall
So we can frame a equation as:
5 adult ticket x cost of 1 adult ticket + 1 student ticket x cost of 1 student ticket = $ 38
[tex]5 \times a + 1 \times s = 38[/tex]
5a + 1s = 38 ------- eqn 2
Let us solve eqn 1 and eqn 2 to find values of "a" and "s"
Multiply eqn 2 by 10
50a + 10s = 380 ---- eqn 3
Subtract eqn 1 from eqn 3
50a + 10s = 380
4a + 10s = 58
( - ) --------------------
46a = 322
a = 7Substitute a = 7 in eqn 1
4a + 10s = 58
4(7) + 10s = 58
28 + 10s = 58
10s = 58 - 28
10s = 30
s = 3Thus cost of 1 adult ticket is $ 7 and cost of 1 student ticket is $ 3
Sue makes 60 tuna sandwiches for a class outing. She makes 4 sandwiches from each can of tuna. She uses 15 cans of tuna.
How many cans of tuna would Sue need if she made 3 sandwiches from each can?
She would need _____ cans.
Answer:
20 cans of tuna.
Step-by-step explanation:
4 x 15 = 60
3 x ? = 60
3 x 20 = 60
16x^4 - 144x^2
How to factorise this question and which identity should we use
The factored form of given expression is:
[tex]16x^2(x-3)(x+3)[/tex]
Step-by-step explanation:
The identity that can be used to factorize the given expression is:
[tex]a^2-b^2 = (a+b)(a-b)[/tex]
Given
[tex]16x^4-144x^2[/tex]
As 16 is a factor of both terms
[tex]=16x^2(x^2-9)[/tex]
Using the identity
[tex]=16x^2[(x)^2-(3)^2]\\=16x^2[(x-3)(x+3)][/tex]
Hence,
The factored form of given expression is:
[tex]16x^2(x-3)(x+3)[/tex]
Keywords: Factorization, polynomials
Learn more about polynomials at:
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solve each proportion using cross product property
Using the cross product property on this proportion gives us the following equation:
6 (3x + 3) = 7 (x + 16)
Use the distributive property
18x + 18 = 7x + 112
Subtract both sides by 7x
11x + 18 = 112
Subtract both sides by 18
11x = 94
Divide both sides by 11
x = 94/11
This fraction is already fully simplified and cannot be simplified further. This should be your answer.
Let me know if you need any clarifications, thanks!
Answer:
Step-by-step explanation:
6(3x+3) = 7(x+16)
18x+18=7x+112
-7 on both sides
11x+18=112
-18 on both sides
11x/11 = 94/11
x=8.5
Consider the formula W=Fd, where
• W represents work
• F represents force and has units of Newtonsand
•D represents distance and has units of meters (m),
Select an appropriate measurement unit for work.
Plz look at pic
Answer:
Option B [tex]\frac{Kg*m^2}{s^2}[/tex]
Step-by-step explanation:
we know that
The formula to calculate the work is equal to
[tex]W=Fd[/tex]
where
W represents work
F represents force
d represents distance
The units are
[tex]F=(\frac{Kg*m}{s^2})[/tex] ---> Newtons
[tex]d=m[/tex] ---> meters
substitute the units in the formula
Remember that when multiply exponents with the same base, adds the exponents and maintain the same base
[tex](m)(m)=m^{1+1}=m^2[/tex]
so
[tex]W=(\frac{Kg*m}{s^2})(m)=(\frac{Kg*m^2}{s^2})[/tex]
Answer:
B
Step-by-step explanation:
the surface area of a cuboid is 95cm² and its lateral surface area is 63cm². find the area of its base
Answer:
The Area of the base is 16 cm² .
Step-by-step explanation:
Given as :
The surface area of the cuboid = x = 95 cm²
The lateral surface area of the cuboid = y = 63 cm²
Let The Area of the base = z cm²
Now, Let The length of cuboid = l cm
The breadth of cuboid = b cm
The height of cuboid = h cm
According to question
∵ The surface area of the cuboid = 2 ×(length × breadth + breadth × height + height × length)
Or, x = 2 ×(l × b + b × h + h × l)
Or, 95 = 2 ×(l × b + b × h + h × l)
Or, (l × b + b × h + h × l) = [tex]\dfrac{95}{2}[/tex] ....1
Similarly
∵lateral surface area of the cuboid = 2 ×(breadth × height + length × height)
Or, y = 2 ×(b × h + l × h)
Or, 2 ×(b × h + l × h) = 63
Or, (b × h + l × h) = [tex]\dfrac{63}{2}[/tex] ......2
Putting value of eq 2 into eq 1
so, (l × b + [tex]\dfrac{63}{2}[/tex] ) = [tex]\dfrac{95}{2}[/tex]
Or, l × b = [tex]\dfrac{95}{2}[/tex] - [tex]\dfrac{63}{2}[/tex]
Or, l × b = [tex]\dfrac{95 - 63}{2}[/tex]
i.e l × b = [tex]\dfrac{32}{2}[/tex]
so, l × b = 16
Now, Again
∵The Area of the base = ( length × breadth ) cm²
So, z = l × b
i.e z = 16 cm²
So, The Area of the base = z = 16 cm²
Hence,The Area of the base is 16 cm² . Answer
10)_
If you multiply six positive numbers, the product's sign will be . If you mump
negative numbers, the product's sign will be
a) Positive; Negative
b) Negative; Negative
c) Positive; Positive
d) Negative; Positive
on will be. If you multiply six
Answer:
Step-by-step explanation:
Explanation:
The product of two positive numbers is always positive.
So product of All positive numbers will be always positive.
For Example
( + ) × ( + ) = ( + )
The product of two negative number is always positive.
So product of even negative numbers will be always positive
For example
( - ) × ( - ) = ( + )
Also product of negative and positive is also given as a negative
( - ) × ( + ) = ( - )
and
( + ) × ( - ) = ( - )
Let the Six Positive numbers be
a, b ,c , d, e, f
So the Product of Six Positive numbers will be
[tex](+a)\times (+b)\times (+c)\times (+d)\times (+e)\times (+f)=\textrm{Positive Number}[/tex]
Let the Six Negative numbers be
-a, -b ,-c , -d, -e, -f
So the Product of Six Negative numbers will be
[tex](-a)\times (-b)\times (-c)\times (-d)\times (-e)\times (-f)=\textrm{Positive Number}[/tex]
Therefore the Product's Sign will be
a) Positive ; Positive
Answer:
c) Positive; Positive
Step-by-step explanation:
As we know it is a basic rule in mathematics, that if positive is multiplied by positive it gives a positive result always. So hence, from this rule it is proved that if we multiply 6 positive numbers, we will be getting the product which will be having positive sign. And in the second part of the questions, answer is that if we multiply 6 negative numbers then the sign remains positive as we know it is also a basic rule in mathematics that when 2 negative numbers are multiplied by each and other then it will give a positive product. So the answer will remain 'c) Positive; Positive''
chris bought a cup of hot chocolate does his cup probably hold 400 liters or 400 milliliters of hot chocolate
Answer:
Millileters
Step-by-step explanation:
If it held 400 liters, it would be a pretty gigantic cup
Answer:
400 millieters
Step-by-step explanation:
because a cup is measured in milliters
4^-3 × 4^2 × 4^5 = 4^?
The value of the missing exponent is 4^10?
True or false
Answer:
[tex] {4}^{ - 3} \times {4}^{2} \times {4}^{5} = {4}^{ - 3 +2 + 5} = {4}^{4} [/tex]
False. The missing exponent is 4.
What is the remainder when 4x^3+2x^2-18+38/x-3
Answer:
110
Step-by-step explanation:
You want the remainder from the division ...
[tex]\dfrac{4x^3+2x^2-18x+38}{x-3}[/tex]
RemainderThe remainder theorem tells you the remainder of ...
f(x)/(x -a)
is f(a).
We can compute f(a) directly, or we can do it using synthetic division. The attachment shows the synthetic division approach.
If we want to evaluate f(x), it is convenient to write it in Horner Form:
f(x) = 4x³ +2x² -18x +38 = ((4x +2)x -18)x +38
Then, for x = 3, this is ...
((4·3 +2)·3 -18)·3 +38 = (14·3 -18)·3 +38 = 24·3 +38 = 110
The remainder from the division is 110.
-5(-5w+3v-2) how do I use distributive property to remove the parentheses
Answer:you would times everything on the inside by 5 im pretty sure
Step-by-step explanation:
How do you write the subtraction problem -8-5 as an addition problem?
Answer - 8+(-5)= -13
Step-by-step explanation:
87th term of 12,0,-12
Answer:
[tex]a_{87} = -1020[/tex]
Step-by-step explanation:
Given:
The given AP is.
12,0,-12,......
[tex]n=87[/tex]
The first term of an AP [tex]a=12[/tex]
Common difference [tex]d=0-12=-12[/tex]
We use the the formula for nth term of an AP.
[tex]a_{n} = a+(n-1)d[/tex]
for 87th term
[tex]a_{87} = 12+(87-1)(-12)[/tex]
[tex]a_{87} = 12+(86)(-12)[/tex]
[tex]a_{87} = 12+(-1032)[/tex]
[tex]a_{87} = 12-1032[/tex]
[tex]a_{87} = -1020[/tex]
Therefore, The 87th term of given series is -1020.
Alia works for 18.3 hours and earns $585.60. What does Alia earn per hour?
To calculate Alia's hourly wage, you divide the total amount she earned ($585.60) by the total number of hours she worked (18.3 hours), which results in approximately $32 per hour. This question is related to the subject of Mathematics, specifically rates and ratios.
Explanation:The subject of this question is Mathematics, specifically the sub-topic of rates and ratios, which includes calculating earnings per hour.
To calculate Alia's earnings per hour, we need to divide her total earnings by the number of hours she worked. Here's a step-by-step explanation:
First, identify the total amount earned and the total hours worked. In this case, Alia earned $585.60 in 18.3 hours.Next, divide the total earnings by the total number of hours worked. So we do $585.60 divided by 18.3 hours.The result will give you the hourly wage. After performing the division, we find that Alia earns approximately $32 per hour.Learn more about Hourly Wage here:https://brainly.com/question/1582269
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The perimeter of a square depends on the length of its sides. Answer the questions below regarding the relationship between the perimeter of the square and the length of one side of the square.
The perimeter of a square is calculated by multiplying the length of one side by 4.
The perimeter of a square is the sum of all four sides. Since a square has equal sides, you can find the perimeter by multiplying the length of one side by 4. The formula for the perimeter of a square is P=4s, where P is the perimeter and s is the length of one side.
For example, if the length of one side is 5 units, the perimeter would be 4 * 5 = 20 units. If the length of one side is 8 centimeters, the perimeter would be 4 * 8 = 32 centimeters.
Learn more about perimeter here:https://brainly.com/question/31695951
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Question 1) DoorDash charges a fee of $4.25 to deliver food from a local restaurant and $1.35 per mile. Your meal costs $10.47 before
delivery
Which of the following inequalities can be used to find the maximum number of miles, m, the delivery driver can travel so
that you spend no more than $30?
be
A
m
(10.47 +4.25 +1.35) > 30
arbel
B
10.47 +4.25m + 1.35m<30
°C 10.47 +4.25 + 1.35m 2 30
OD 10.47 +4.25 +1.35m 530
Answer:C
Step-by-step explanation: fixed cost = 10.47+4.25
Variable cost =1.35m
Total cost= 10.47+4.25+1.35m<=30
Answer:
Option C 10.47 +4.25 + 1.35m 2 30
Step-by-step explanation:
Data:
DoorDash charges a fee of = $4.25
Fee per mile = $ 1.35
Cost of a meal = $ 10.47
The maximum number of miles is given by:
10.47 + 4.25 + 4.25 < 30
Therefore, option C is correct.
Four soccer teams compete in a tournament. Each team faced each other exactly once with no ties allowed. A team received 1 point for each win.
The results
Team 1 had 1 point
Team 2 had 3 points
Team 3 had 1 point
How many points did team 4 have?
Answer:
1 point
Step-by-step explanation:
The number of games in the tournament is:
₄C₂ = 6
Another way to look at it: Team 1 plays 3 games against Team 2, 3, and 4. Then, Team 2 plays 2 games against Team 3 and 4 (Team 2 already played Team 1). Finally, Team 3 plays a game against Team 4. So the total is 3 + 2 + 1 = 6.
If there's a total of 6 games, then there's a total of 6 points. So if x is the number of points Team 4 has:
x + 1 + 3 + 1 = 6
x + 5 = 6
x = 1
Team 4 has 1 point.
A square has an area of 44.89in^2. How do you get the length of the diagonal of the square?
Answer:
[tex]6.7\sqrt{2}\ in[/tex]
Step-by-step explanation:
Let x inches be the length of the side of the square. The area of the square is
[tex]x\cdot x=x^2\ in^2[/tex]
Then
[tex]x^2=44.89\\ \\x=6.7\ in[/tex]
By the Pythagorean theorem,
[tex]d^2=6.7^2+6.7^2\\ \\d^2=44.89+44.89\\ \\d^2=89.78\\ \\d=\sqrt{89.78}=6.7\sqrt{2}\ in[/tex]
Find the length of a side by taking the square root of the area:
Side = sqrt44.89 = 6.7 inches.
Now to find the length of the diagonal multiply the side length by the sqrt of2:
Diagonal = 6.7Sqrt(2) ( exact length)
As a decimal= 9.4752
The owner of a chain of 12 restaurants wants to conduct a survey to determine whether his employees are properly informed by the location manager about safety procedures. Complete the statements below to identify the samples as random or non-random. If the owner surveys employees only at the most popular location and it’s likely all employees at each location were given the same safety information, the sample is . If the owner surveys the same number of employees at each of his restaurants, the sample is .
1. non-random and biased.
2. random and unbiased.
Solve (-7/3)x - 3 = -52
Answer: x = 21
Step-by-step explanation:
look at the picture
Help me please and explain
Check the picture below.
Which set(s) of points show x in DIRECT PROPORTION to y?
A) {E, C, B} only
B) {G, C, A} only
C) {F, E, D} and {E, C, B} only
D) {F, G, H} and {G, C, A} only
Answer: OPTION D.
Step-by-step explanation:
For this exercise it is important to remember that:
1. Direct proportion equations have the following form:
[tex]y=kx[/tex]
Where "k" is the constant of proportionality.
2. The graph of Direct proportions is an straight line that passes through the origin.
Observe the picture attached.
If you join the points G, C and A, you get a straight line that passes through the origin,
If you join the points F, G and H, you also get a straight line that passes through the origin,
Therefore, the sets of points show "x" in Direct proportion to "y", are:
[tex]\{F, G, H\}[/tex] and [tex]\{{G, C, A}\}[/tex]
Answer:D){F, G, H} and {G, C, A} only
Step-by-step explanation:
in the following figure DE||BC AD=4cm DB=6cm AE=5cm then the value of EC is
Answer:
[tex]ec = \frac{6 \times 5}{4} = 7.5 [/tex]
S4) The data can be modeled by the regression line y = 1.2x + 3.5. What is the residual at
=5?
The residual is 1.5
Step-by-step explanation:
Given the regression line equation as : y=1.2x +3.5
The formula for residual = Observed y-value - Predicted y-value
This gives the vertical distance from the actual plotted point to the point on the regression line. You should find how far the data fall from the regression line.
In this case, at y=5, from the graph, to get the vertical distance, perform subtraction as;
5.0 - 3.5 = 1.5
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Keywords : residual, regression line, modeled, data
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Evaluate (24 + 2y) + (7y), if y=4
(24 + 2y) + (7y)
(24 + 8) + 28
32 + 28
60
Answer:
60
Step-by-step explanation:
(24 + 2y) + (7y)
(24 + 2 x 4) + (7 x 4)
(24 + 8) + (28)
32 + 28 = 60
- Make Sense and Persevere If x represents the number
of months since the beginning of 2016, and y represents
the total precipitation to date, predict the amount of
precipitation received between the end of March and
the end of June. MP.1
Pred
Total Precipitation
(in.)
0 2 4
Months Si
Answer:
5,46 inches per months
Step-by-step explanation:
1 year = 12 months
The average precipitation per month is :
65,52 inches ÷ 12 = 5,46 inches per months
HOPE THIS HELPED ;3
The predicted amount of precipitation received between the end of March and the end of June is 0 inches.
Explanation:To predict the amount of precipitation received between the end of March and the end of June, we need to find the difference in total precipitation between those two months. According to the given information, the total precipitation in inches for each month is as follows:
March: 4 inches
April: 2 inches
May: 0 inches
June: 4 inches
To find the amount of precipitation received between the end of March and the end of June, we can subtract the total precipitation at the end of March from the total precipitation at the end of June:
Total precipitation at the end of June - Total precipitation at the end of March = 4 inches - 4 inches = 0 inches
Therefore, the predicted amount of precipitation received between the end of March and the end of June is 0 inches.
I'm having trouble with these problems. and my paper is due tomorrow. please help
Answer:
Step-by-step explanation:
There are (42)3 ⋅ 40 horses on a stud farm. What is the total number of horses on the farm?
Answer:
5040
Step-by-step explanation:
When a number is in the Parenthesis that means you multiply. First you do 42*3 The answer would be 126. Since there is another Multiplication sign you just plug in your quotient (answer) into the problem. Now the equation is 126*40. 126*40=5040
Answer:
4^6
Step-by-step explanation:
Which has a positive value in Quadrant III?
A) Cosine only
B) Sine only
C) Tangent only
D) Cosine, Sine, and Tangent
Answer: THE ANSWER IS B (Sine ONLY)
Step-by-step explanation:i just did it on USAtestprep
plz answer which is it from the 4 choices
Answer:
Option 3
Step-by-step explanation:
we know that
The solution show in the graph represent the interval [4,∞)
All real numbers greater than or equal to 4
In a number line the solution is the shaded area at right of x=4 (closed circle)
The number 4 is included in the solution set
therefore
Option 3
Law of cosines.Anyone good in Trigonometry?
Answer:
[tex]c=11.8\ units[/tex]
Step-by-step explanation:
we know that
The formula of law of cosines is equal to
[tex]c^2=a^2+b^2-2(a)(b)cos(C)[/tex]
where
a, b and c are sides. C is the angle opposite side c
In this problem we have
[tex]a=3\ units\\b=10\ units[/tex]
[tex]C=120^o[/tex]
substitute the given values
[tex]c^2=3^2+10^2-2(3)(10)cos(120^o)[/tex]
[tex]c^2=109-(60)cos(120^o)[/tex]
[tex]c^2=109-(60)(-0.5))[/tex]
[tex]c^2=109+30[/tex]
[tex]c^2=139[/tex]
[tex]c=11.8\ units[/tex]