Answer:
Senior citizen tickets = 9
Student tickets = 10
Step-by-step explanation:
We begin by converting the question into simultaneous linear equations;
Senior citizen tickets = a
Student tickets = b
4a + 6b = 96
8a + 13b = 202
to find a,
if 4a +6b = 96
a = 96/4 - 6b/4
a = 24 - 1.5b
We now substitute this into the second equation
8(24 - 1.5b) + 13b = 202
192 - 12b + 13b = 202
b = 202 - 192
b = 10
We now put the value of b in either equation
4a + 6b = 96
4a + 6(10) = 96
4a + 60 = 96
4a = 96 - 60
4a = 36
a = 9
From a group of 5 candidates, an environmental committee of 3 people is selected. How many different committees are possible?
Therefore possible committees are [tex]^5C_3[/tex] =10
Step-by-step explanation:
Given , from a group of 5 candidates , an environmental committee of 3 people is selected.
Therefore possible committees are [tex]^5C_3[/tex] =10
Albert rode to the park at 12 mph and then back home at 20 mph. If the round trip took 4 hours and it is 30 miles each way, how long did the ride to the park take?
Answer:
It took Albert 2 1/2 hours to ride to the park
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Speed of Albert to the park = 12 mph
Speed of Albert back home = 20 mph
Total time of the round trip = 4 hours
Distance each way = 30 miles
2. How long did the ride to the park take?
Let's recall that the formula of speed is:
Speed = Distance/Time, therefore Time = Distance/Speed
Time it took Albert to ride to the park = 30/12
Time it took Albert to ride to the park = 5/2 = 2 1/2 hours
Time it took Albert to ride back home = 30/20
Time it took Albert to ride back home = 3/2 = 1 1/2 hours
It took Albert 2 1/2 hours to ride to the park
What is the measurement of Complement of 33°
Answer:
The complement of 33 is the angle that when added to 33 forms a right angle
Step-by-step explanation:
it is un needed for a explanation
8
Factor x2 + 12x + 35.
x2 + 12x + 35 =
Answer:
(x + 7) (x + 5)
Step-by-step explanation:
Factor the following:
x^2 + 12 x + 35
The factors of 35 that sum to 12 are 7 and 5. So, x^2 + 12 x + 35 = (x + 7) (x + 5):
Answer: (x + 7) (x + 5)
what is the area of the composite figure? Use 3.14 for π
Answer:
80.52
Step-by-step explanation:
For triangle it is
100-36=64 Root 64=8
24cmsquared
for the half cirlce it is
18pie=56.52
Please help me on this I’m super stuck
Answer:
BC = 3.1666
Step-by-step explanation:
To solve this you need to know that cosine∅ = adjacent/hypotenuse. We already know that hypotenuse = 5 and that ∅ = 70*. By substituting these in you will get cosine 70* = adjacent/5. Evaluate cosine 70* on the calculator and get 0.633... Multiply both sides by 5 and get adjacent is about equal to 3.1666. Because BC is the adjacent side of the triangle, this is the length of BC.
If you invested $500 at 5% simple interest for 2 years, how much interest do you earn? Show work and answer in complete sentences to earn full credit.
If you invest $500 at 3% compounded monthly for 2 years, how much interest you do earn? Show work and answer in complete sentences to earn full credit.
Which would you rather do?
Answer:
i) $500 at 5% simple interest for two years.
Interest = 550 - 500 = $50
ii) $500 at 3% compounded monthly for 2 years.
Interest = 530.88 - 500 = $30.88
I would take the first option i)$500 at 5% simple interest for two years.
Step-by-step explanation:
i) $500 at 5% simple interest for two years.
Initial amount, P = $ 500
Rate of interest, r = 0.05
Time in years, t = 2
Therefore Final amount A = P(1 + rt) = 500(1 + (0.05 2) ) = $550
Therefore Interest = 550 - 500 = $50
ii) $500 at 3% compounded monthly for 2 years
Initial or Principal Amount, P = $500
Rate of interest, r =0.03
number of conversions, m = 12
Time in years, t = 3
Therefore final amount, = $530.88
Therefore Interest = 530.88 - 500 = $30.88
I would take the first option i) $500 at 5% simple interest for two years.
Mariela bought 15 pounds of birdseed for $10.00. Mark bought 12 pounds of birdseed for $8.00. Daryl bought 18 pounds of birdseed for $12.00. If the cost per pound remains the same, what should be the cost of one pound of birdseed?
Answer:
The cost for one pound of birdseed is $0.67
Step-by-step explanation:
Use Mariela's example first
To find the cost per pound, get the pounds to 1.
15 pounds = $10.00 Divide both sides by 15 to get 1 pound
1 pound = $0.67
Use Mark's example to see if it is the same rate
12 pounds = $8.00 Divide both sides by 12 pounds to get one pound
1 pound = $0.67
Use Daryl's example to prove the other answers
18 pounds = $12.00 Divide both sides by 8 pounds to get one pound
1 pound = $0.67
Reflecting the graph of y = sinx across the y-axis is the same as reflecting it across
the x-axis.
Answer:
The statement is true.
Step-by-step explanation:
Given : Reflecting the graph of y = sin x across the y-axis is the same as reflecting it across the x-axis.
To find : Is this statement true or false?
Solution:
Rules of reflection :
Along across y-axis if we have a point
So, y=sinx
The reflection across y-axis→ .......[1]
Along across x-axis if we have a point
so, y=sinx
The reflection across x-axis → .....[2]
Hence, [1] and [2] both of them are equal
Therefore, the statement is true.
Answer:
The answer is true for A P E X
Step-by-step explanation:
A teacher wrote the equation 3y + 12 = 6x on the board. For what value of b would the additional equation 2y = 4x +
b form a system of linear equations with infinitely many solutions?
b= -8
b=-4
b = 2
b= 6
Answer:
The answer A) b=-8
Step-by-step explanation:
Answer:
b = -8
Step-by-step explanation:
What is the answer to 5(1 + 5n)
Answer: 5 + 25n
Explanation: Let's simplify this problem using the distributive property.
In this problem, the 5 "distributes" through the parentheses which means that it multiplies by each of the terms inside.
So we have 5(1) + 5(5n) which simplifies to 5 + 25n.
Which of the following pairs of numbers contain like fractions?
6/7 and 1 5/7
3/2 and 2/3
5/6 and 10/12
3 1/2 and 4 3/4
Answer:
6/7 and 1 5/7
Step-by-step explanation:
Answer:
6/7 and 1 5/7
5/6 and 10/12= 5/6
Sabra joins a cooking club for $8.50 and pays $6.25 each month. She also joins a movie club for $12 and pays $3.75 each month. Write an expression that represents the total amount of money Sabra spends on both clubs after m months. Then enter the simplified expression in the boxes.
+
m
Simplified expression for total amount spent is 10(2.05 + m)
Step-by-step explanation:
Step 1: Write expression for expense on joining cooking club for m months.Expense = 8.50 + 6.25 × m
Step 2: Write expression for expense on joining movie club for m months.Expense = 12 + 3.75 × m
Step 3: Calculate the total amount spent on both clubsTotal Amount = 8.50 + 6.25m + 12 + 3.75m = 20.5 + 10m = 10(2.05 + m)
Sabra spends a total amount represented by the simplified expression 20.50 + 10m after m months on both the cooking and movie clubs.
To find the total amount of money Sabra spends on both clubs after m months, we need to consider the costs of joining each club and the ongoing monthly fees.
Sabra's cooking club costs $8.50 to join and $6.25 per month. This can be represented by the expression:
8.50 + 6.25mSabra's movie club costs $12 to join and $3.75 per month. This can be represented by the expression:
12 + 3.75mTo find the total amount spent on both clubs, we sum these expressions:
(8.50 + 6.25m) + (12 + 3.75m)Simplifying this expression, we get:20.50 + 10mSo, the total amount of money Sabra spends on both clubs after m months can be expressed as 20.50 + 10m
How many places do you need to move the decimal to the right to write the
number below in scientific notation?
0.00000092
A.8 B.7 C.2 D.6
Answer:
Step-by-step explanation:
For a number to be written in standard form, it must be in a format
A×10^n
Now, n can be positive or negative, i.e n is an integer
Also, A must be between 0 and 10. It must not be outside those number
i.e 0<A<10
Therefore, to answer the question
0.00000092
The point will start to move for the negative and it will stop after the first number
If it is moving rightward, n is negative.
if it is moving leftward, n is positive
So,
9.2×10^-7 is the answer.
Then the answer is B
n=7 it moves 7 time to get to 9.2
Answer:
B.7
Step-by-step explanation:
The range of scientific notation is
0.9999999 to 9.999999999
What is an written expression for 20+5×9
Answer:
Five times nine plus twenty
Step-by-step explanation:
Just remember the order of operations... multiplication and division are done first before adding and subtracting.
Is y=15/x a linear function
Answer:
NO
Step-by-step explanation:
The equation y = 15/x is not a linear function. A linear process follows the form y = a + bx and graph as a straight line. The given equation doesn't track that form or behavior; hence, it is not linear.
Explanation:No, the equation y = 15/x is not a linear function. In Mathematics, a linear function is defined by the equation y = a + bx, where a is the y-intercept, b is the slope, x is the independent variable, and y is the dependent variable. In this equation, the relationship between x and y is direct, meaning if x increases or decreases, y will also increase or decrease at a constant rate.
However, in the equation y = 15/x, the relationship between x and y is inverse. If x increases, y decreases, and vice versa. Furthermore, the form of the equation doesn't follow the standard form of a linear equation (y = a + bx) because the x variable is in the denominator. Therefore, it is not linear because it will not graph as a straight line.
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The equation 3y=5x represents a proportional relationship. what is the constant of proportionality for this relationship
The constant of proportionality for this relationship is [tex]\frac{5}{3}[/tex]
Step-by-step explanation:
Proportional relationship is the relation between two variables that vary directly with each other
If x and y are proportion, then y = k x, where k is the constant of proportionalityIf x and y are proportion, then [tex]\frac{y}{x}=k[/tex], where k is the constant of proportionality∵ The equation is 3 y = 5 x
∵ x and y are proportional
- That means y = k x, where k is the constant of proportionality
∴ Put the equation in the form y = k x
- Divide both side by the coefficient of y
∵ The coefficient of y is 3
∴ Divide both sides of the equation by 3
∴ y = [tex]\frac{5}{3}[/tex] x
- The value [tex]\frac{5}{3}[/tex] is constant
∴ k = [tex]\frac{5}{3}[/tex]
∵ k represents the constant of proportionality
∴ The constant of proportionality = [tex]\frac{5}{3}[/tex]
The constant of proportionality for this relationship is [tex]\frac{5}{3}[/tex]
Learn more:
You can learn more about the proportional relationship in brainly.com/question/10708697
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