The price of one senior citizen ticket is $7 and the price of one child ticket is $8.
What are the linear equations that represent this question?s + 13c = 111 equation 1
12s + 9c = 156 equation 2
Where:
c = price of one child ticket s = price of one senior citizen ticket What is the price of one children's ticket?Multiply equation 1 by 12
12s + 156c = 1332 equation 3
Subtract equation 2 from equation 3
1176 = 157c
c = $8
What is the price of one senior citizen's ticket?
Substitute for c in equation 1:
s + 13(8) = 111
s = 111 - 104
s = $7
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ou toss a coin (heads or tails), then spin a three-color spinner (red, yellow, or blue). Complete the tree diagram, and then use it to find a probability.
1. Label each column of rectangles with "Coin toss" or "Spinner."
2. Write the outcomes inside the rectangles. Use H for heads, T for tails, R for red, Y for yellow, and B for blue.
3. Write the sample space to the right of the tree diagram. For example, write "TY" next to the branch that represents "Toss a tails, spin yellow."
4. How many outcomes are in the event "Toss a tails, spin yellow"? (1 point)
5. What is the probability of tossing tails and spinning yellow? (1 point)
The tree diagram that represents the events is an illustration of probability and combination
The tree diagramTo draw the tree diagram, we make use of the following representations:
H for heads, T for tails, R for red, Y for yellow, and B for blue.See attachment for the tree diagram.
The sample space and the outcomesFrom the tree diagram, the sample space is as follows:
S = {HR, HY, HB, TR, TY, TB}
The number of outcomes that represents "Toss a tail, spin yellow"This is represented as: TY
From the sample space above, we have:
TY = 1
Hence, the number of outcomes that represents "Toss a tail, spin yellow" is 1
The probabilityWe have:
TY = 1
Sample size = 6
Hence, the of tossing tails and spinning yellow is 1/6
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Does anybody know how to solve this?
The area of the rectangle in the form of a polynomial is 40(x² + 6x + 5). If the width is 160 ft, then the area of the rectangle is 57,600 square ft.
What is a rectangle?It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a rectangle, opposite sides are parallel and equal and each angle is 90 degrees. And its diagonals are also equal and intersect at the mid-point.
If the length and width of the rectangle are (10x + 10) and (4x + 20). Then the area of the rectangle will be
Area = (10x + 10)(4x + 20)
Area = 40x² + 200x + 40x + 200
Area = 40x² + 240x + 200
Area = 40(x² + 6x + 5)
If the width is 160 feet then the value of x will be
4x + 20 = 160
4x = 140
x = 35
Then the area of the rectangle will be
Area = 40(35² + 6 × 35 + 5)
Area = 40(1225 + 210 + 5)
Area = 40 (1440)
Area = 57,600 square ft
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Alejandro was picked by this teacher to find the integer that has the square root closest to 7, without going over. he wrote 52 on the bored. was he correct? explain your reasoning.
Considering that the square root of 49 is 7, and 52 > 49, Alejandro was not correct, as the correct integer is of 48.
What is the integer that has the square root closest to n, without going over?The integer that has square root n is given by:
S(n) = n².
Hence the closest is given by:
C(n) = n² - 1.
In this problem, we have n = 7, hence:
C(7) = 7² - 1 = 48.
Which means that Alejandro was not correct.
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Peter is planting a rectangular garden. The length is 15 yards longer than the width. Jorge is planting a square garden. The sides of Jorge's garden are equal to the width of Peter's garden. What is the ratio of the area of Peter's garden to the area of Jorge's garden? Use this ratio to find the ratio of the areas if the width of Peter's garden is 32 yards.
x + 32/x ; 32/15
x-32/x ; 32/15
x+15/x ; 47/32
x-15/x ; 47/32
If the width of peter's garden is 32 yards, the ratio of the areas is 47: 32
Area of a rectangle.area of rectangle = lw
where
l = lengthw = widthTherefore,
Peter rectangular garden
l = 15 + xJorge is planting a square garden. The sides of Jorge's garden are equal to the width of Peter's garden.
Therefore,
x = side of Jorge gardenThe ratios are as follows;
(15 + x)x : x²
Therefore, if the width of peter's garden is 32 yards, the ratio of the areas is as follows:
(15 + 32)32 : 32²
1504: 1024
752: 512
376: 256
94:64
47: 32
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Answer:
(x+15)/x; 47/32
If f(x) = 5x, what is ƒ¹ (x)?
Answer:
15,625
Step-by-step explanation:
If f(x) = 5x then f ¹ you must label all numbers in the equation to make it easier, once done you will have 25(5¹)=125¹
125x125=15,625
The inverse function of the given function is x/5.
What is inverse function?Inverse function is represented by f⁻¹ with regards to the original function and the domain of the original function becomes the range of inverse function and the range of the given function becomes the domain of the inverse function. The graph of the inverse function is obtained by swapping (x, y) with (y, x) with reference to the line y = x.
Given that, f(x)=5x
Now, y=5x
Replace x by y and y by x, we get
x=5y
y=x/5
and f⁻¹(x)=x/5
Therefore, the inverse function of the given function is x/5.
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please help me on this you will get alot of point and brainliest
Answer:
0.8 miles
Step-by-step explanation:
Answer:
5.2 miles
Step-by-step explanation:
Airport to Arcadia is one leg of right triangle = x
Airport to Stafford is leg2 of right triangle = 7.6
9.2 miles is hypotenuse of right triangle
Pythagorean theorem:
x^2 + 7.6^2 = 9.2^2
x = ~ 5.2 miles
HELP ASAP PLSSSSSSS
Clara surveyed the students at her school to find out if they like pies and/or sandwiches. The results of her survey are shown in the two-way table below:
Like Pies
Do Not Like Pies
Total
Like Sandwiches
25
43
68
Do Not Like Sandwiches
26
6
32
Total
51
49
100
If a student does not like sandwiches, what is the probability that student also does not like pies?
81.3%
26.0%
23.1%
18.8%
Answer:
18.8%
Step-by-step explanation:
For calculating this, focus on one part of the table :
The row where students do not like sandwichesThere are 32 students who do not like sandwiches, and 6 of them do not like pies. Take this a proportion :
P (does not like pies, do not like sandwiches) = 6/32P = 3/16P = 18.8%Students who don't like sandwiches also don't like pie is the 2 nd box on 2 nd line
Probability
P(E)=6/32P(E)=6/32×100=3/16×100=18.8%Option D
The base of a ladder is placed 2.8m away from a tree that is 4.5m tall. The end of the ladder touches the top of the tree. Calculate the length of the ladder.
Answer:
The length is 7.3m
Step-by-step explanation:
The end of the ladder touches the top of the tree when kept at 2.8m away from the tree.
The Tree is 4.5m tall
The length of the ladder will be: 2.8+4.5 = 7.3
What is the median of this data set?
{12, 8, 9, 12, 10, 13,8}
Enter your answer in the box.
Answer:
10
Step-by-step explanation:
HELP PLEASE!!
5⁸/5³=
a. 5^-5
b. 1¹¹
c. 5⁵
d. 5 ¹¹
Answer:
C
Step-by-step explanation:
[tex] \frac{ {5}^{8} }{ {5}^{3} } \\ [/tex]
Now you may reduce the fraction
[tex] = {5}^{5} [/tex]
Simplify.
4(v-5)-7v pls help quick
Answer:
-3v-20
Step-by-step explanation:
chef johnson used 4 1/2 of flour to make 4 fruitcakes. How many cups of flour are needed for 1 fruitcake
Answer:
1 1/8 cups of flour
Step-by-step explanation:
hi!
If Chef Johnson needs 4 1/2 cups of flour to make 4 fruitcakes and he wants to make one, he has to divide the recipe by 4. 4 1/2 / 4= 1 1/8
Solve for d -6 = d/3
Answer:
-18
Step-by-step explanation:
sin(-17pi/6)
How do I solve this
Answer:
if you have a graphing calculator you can just plug the whole equasion in. the anser I got was -0.1547307191
Step-by-step explanation:
to get pie you have to hit second and then ^
[tex]f(n)=3^n[/tex]
find expressions for [tex]f(n+3)[/tex] and [tex]f(n+1)[/tex]
hence find the value of [tex]k[/tex] such that [tex]f(n+3)-f(n+1)= kf(n)[/tex] where k ∈ N
Answer:
[tex]24(f(n))[/tex]
Step-by-step explanation:
[tex]f(n+3) = 3^{n+3}\\f(n+1) = 3^{n+1}[/tex]
so
[tex]f(n+3) - f(n+1) = 3^{n+3} - 3^{n+1}[/tex]
[tex]= 27(3^n) - 3(3^n)[/tex]
[tex]= 24(3^n)[/tex]
[tex]= 24(f(n))[/tex]
hope this helped! :)
Solve:
2x-1/x+4 is greater than or equal to 0
The solution range of the given inequality is (-∞, -4.121) and (0.121,∞)
How to solve the inequality?
Here we want to solve:
[tex]2x - 1/(x + 4) \geq 0[/tex]
To solve this, we multiply both sides by (x + 4) so we get:
[tex]2x*(x + 4) - 1 \geq 0\\\\2x^2 + 8x - 1 \geq 0[/tex]
Now we can solve it graphically, below we have:
There we can see that the solution range is (-∞, -4.121) and (0.121,∞), the regions where the graph is equal or above the horizontal axis.
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Sela is making 400 scones.
she use butter ,sugar and flour in the ratio 2:1:9
here the cost of those ingredients
butter-2.50 per 500g
sugar-1.60 per kilogram
flour-60p per 1.5kg
the total mass of the butter ,sugar and flour in each scone is 30g
work out the total cost of these ingredients for the 400
scones
Answer:
£15.20
Step-by-step explanation:
butter : sugar : flour = 2 : 1 : 9
Total mass for 1 recipe = 30 g
2 + 1 + 9 = 12
12x = 30
x = 30/12
x = 2.5
For 1 scone:
butter = 2x = 2(2.5) g = 5 g
sugar = x = 2.5 g
flour = 9x = 9(2.5) g = 22.5 g
Cost for 1 scone:
butter: 5 g × £2.50/(500 g) = £0.025
sugar: 2.5 g × £1.60/(1000 g) = £0.004
flour: 22.5 g × £0.6/(1500 g) = £0.009
Cost for 1 recipe = £0.025 + £0.004 + £0.009 = £0.038
Cost for 400 scones = 400 × £0.038 = £15.20
Answer: £15.20
A diner is serving a special lunch combo meal that includes a drink, a main dish, and a side. Customers can choose among 5 drinks, 4 main dishes, and 5 sides. How many different combo meals are possible? Select from the drop-down menu to correctly complete the statement Customers can create Choose... different lunch combo meals. 4 A 1 2 3 4 5. oc 9
Since the customers can choose among 5 drinks, 4 main dishes, and 5 sides. there 100 different combo meals are possible.
Since order is not important we use combination to solve the problem
What is combination?This is the number of ways in which x objects can be selected out of n objects. It is given mathematically as ⁿCₓ = n!/x!(n - x)!
The number of different combo mealsNow, given that the customer can choose among 5 drinks, 4 main dishes, and 5 sides.
There are ⁵C₁ ways of choosing the drinks.
So, ⁵C₁ = 5!/1!(5 - 1)!
= 5!/1!/4!
= 5
There are ⁴C₁ ways of choosing the main dishes.
So, ⁴C₁ = 4!/1!(4 - 1)!
= 4!/1!/3!
= 4
There are ⁵C₁ ways of choosing the sides.
So, ⁵C₁ = 5!/1!(5 - 1)!
= 5!/1!/4!
= 5
So, total number of ways of choosing the combo meals is
⁵C₁ × ⁴C₁ × ⁵C₁ = 5 × 4 × 5
= 100 ways.
So, there 100 different combo meals are possible.
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Answer: The answer is 100
Step-by-step explanation:
What additional information do you need to prove the triangles are congruent by SAS
Answer:
Step-by-step explanation:
IMPORTANT HELP PLEASE ANSWER IMMEDIATELY!!!!!
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Solve the following equation. Show all your work.
(x/(x−2))+((x−1)/(x+1))=−1
Answer:
Step-by-step explanation:
Find the x-intercept and the y-intercept of the line below. Click on "None" if applicable.
Answer:
a) None
b) (0, -2)
Step-by-step explanation:
The x-intercept is the point at which the line cuts through the x-axis, while the y-intercept in the point at which the line cuts through the y-axis.
a) The line does not cut through the x-axis, thus it has no x-intercept.
b) The line cuts through the y-axis at y= -2, making its y-intercept (0, -2).
The figures below are similar. What is v?
Answer:
v = 16 mm
Step-by-step explanation:
since the figures are similar then the ratios of corresponding sides are in proportion, that is
[tex]\frac{v}{20}[/tex] = [tex]\frac{28}{35}[/tex] ( cross- multiply )
35v = 560 ( divide both sides by 35 )
v = 16
Solve the equation.
7x2 + 5 - x = 6x2 + 10
X =
20
It
Answer:
1 +√21 + 1 - √21
2 2
Step-by-step explanation:
HELP ASAP PLSSSS!!!!
If you need an image im putting it down below
Which line best represents the line of best fit for this scatter plot?
Graph shows numbers from 0 to 10 at increments of 1 on the x axis and numbers from 0 to 18 at increments of 2. Scatter plot shows ordered pairs 1, 1 and 2, 4 and 3, 12 and 4, 6 and 5, 8 and 6, 8 and 7, 12 and 8, 10 and 9, 14 and 10, 18. A line labeled P joins ordered pair 0, 1 and 9, 18. A line labeled Q joins ordered pairs 0, 1 and 10, 16. A line labeled R joins ordered pairs 0, 1 and 10, 10. A line labeled S joins ordered pairs 0, 1 and 10, 6.
Line P
Line Q
Line R
Line S
This line is fairly close to the majority of the points shown. Unfortunately there's an outlier left out, but it isn't too far from the main cluster. The further the outlier is, the more pull it will drag the line away from the main cluster.
Line Q
The suitable line should contain most dots near itQ contains atleast 4 around it.No other has soQ is correct
tim has 4 quarters and 5 pennies. how many cents does tim have?
Answer: $1.05
Step-by-step explanation:
quarters= 25 cents
4 x 25=100 cents
pennies=1 cent
5 x 1 = 5 cents
100+5=$1.05 or 105 cents
Mason has a business selling perfume at the mall. Currently his business has a
balance of -$20.
Which amounts of sales would give Mason's business a positive balance?
Choose ALL that apply.
$15 $35 $21 $29 $30 $19
Answer:
21, 29, 30, 35
Step-by-step explanation:
anything greater than 20 would break even and then give a position balance
PLEASE HELP ME IF YOU DO you will get the most loyal friend and honest and nicest
Answer:
Below:
Step-by-step explanation:
1. 2 15/28
2. 2 7/10
3. 5/6
4. 1 5/12
5. 2 1/12
A 10% increase in cigarette prices has been found to result in a _____ decrease of smokers. a. 2% b. 4% c. 10% d. 20% please select the best answer from the choices provided. a b c d
A 10% increase in cigarette prices has been found to result in a 4% decrease of smokers.
What is the effect of price increase in the demand for cigarettes?An increase in cigarette price will result in a decrease in the demand for cigarettes.
Since more money needs to be spent to but the same product, less consumers can be able to afford it.
Therefore, a 10% increase in cigarette prices has been found to result in a 4% decrease of smokers.
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Sarah is selling brackets and earrings to make money for summer vacation. She earns $2 from each bracket and $3 from each pair of earrings. She needs to make at least $210 what possible combination of brackets and earrings that Sarah can sell to reach her goal
Answer:
$16 dollars because I got it right
Which expression represents the sixth term in the binomial expansion of (5y 3)10?
The expression in the 6th term in the binomial expression is [tex]265781250y^6[/tex]
How to determine the expression in the sixth term?The expression is given as:
(5y + 3)^10
The above expression is a binomial expression, and the xth term can be represented using:
[tex]^nC_x (a)^x * (b)^{n-x}[/tex]
So, we have:
[tex]^{10}C_6 * (5y)^6 * (3)^4[/tex]
Evaluate the combination expression
[tex]210 * (5y)^6 * (3)^4[/tex]
Evaluate the exponents
[tex]210 * 15625y^6 * 81[/tex]
Evaluate the product
[tex]265781250y^6[/tex]
Hence, the expression in the 6th term is [tex]265781250y^6[/tex]
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