Answer:
Senior citizen tickets = $9
Student tickets = $11
Step-by-step explanation:
We begin by converting these into simultaneous linear equation;
Senior citizen tickets = a
Student tickets = b
5a + 9b = 144
14a + 6b = 192
5a = 144 - 9b
a = 144/5 - 9b/5
a = 28.8 - 1.8b
We now substitute this into the first equation
14(28.8 - 1.8b) + 6b = 192
403.2 - 25.2b +6b = 192
-19.2b = 192 - 403.2
b = -211.2/-19.2
b = 11
Put the value of b into either equation
5a + 9b = 144
5a + 9(11) = 144
5a +99 = 144
5a = 144-99
5a = 45
a = 9
2/3 of a year is how many months
Answer:8
Step-by-step explanation:
There are 12 months in a year if you divide by 3 you get 4 and whatever you do to the numerator you have to do the denominator vice versa so you would multiply by four and get eight so it would be eight months
Answer:
2/3 of a year is 8 months
Step-by-step explanation:
rachel spent $3.60 for stamps to mail packages. Some were 30-cent stamps and the rest were 20-cent stamps. The number of 20-cent stamps was 2 less than the number of 30-cent stamps. How many stamps of each kind did rachel buy?
Rachel bought six 20-cent stamps and eight 30-cent stamps.
Step-by-step explanation:
Given,
Amount spent on stamps = $3.60 = 3.60*100 = 360 cents
Let,
x = 20 cent stamps
y = 30 cent stamps
According to given statement;
20x+30y=360 Eqn 1
x = y-2 Eqn 2
Putting value of x from Eqn 2 in Eqn 1
[tex]20(y-2)+30y=360\\20y-40+30y=360\\50y=360+40\\50y=400[/tex]
Dividing both sides by 50
[tex]\frac{50y}{50}=\frac{400}{50}\\y=8[/tex]
Putting y=8 in Eqn 2
[tex]x=8-2\\x=6[/tex]
Rachel bought six 20-cent stamps and eight 30-cent stamps.
Keywords: linear equation, substitution method
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Final answer:
Rachel bought 8 thirty-cent stamps and 6 twenty-cent stamps. We solved a system of equations representing the cost of the stamps and their quantity relationship to determine the numbers.
Explanation:
Rachel spent $3.60 for stamps to mail packages, buying 30-cent stamps and 20-cent stamps. The number of 20-cent stamps was 2 less than the number of 30-cent stamps. To solve this, we can use a system of equations to represent the total cost and the relationship between the number of stamps:
Let x be the number of 30-cent stamps.
Let y be the number of 20-cent stamps.
Based on the information given:
0.30x + 0.20y = 3.60 (Total cost equation)
y = x - 2 (Relationship between the stamps)
We substitute the second equation into the first equation:
0.30x + 0.20(x - 2) = 3.60
0.30x + 0.20x - 0.40 = 3.60
0.50x = 4.00
x = 8
Now we solve for y using the second equation:
y = 8 - 2
y = 6
So Rachel bought 8 thirty-cent stamps and 6 twenty-cent stamps.
on the last friday in may, one fourth of the 280 students in a school were away on a field trip how many students were on the field trip
If a figure was dilated using a scale factor of 2/3, the first step in mapping it back
onto itself is to dilate the new figure with a scale factor of ?
2/3
2
3
3/2
Answer:3/2
Step-by-step explanation:
A line intersects the points (14, -3) and (9, -11).
Find the slope of the line and simplify completely.
Slope =
Answer:
8/5 or 1 3/5
Step-by-step explanation:
Which of the following are necessary when proving that the diagonals of a
rectangle are congruent? Check all that apply.
o A. Opposite sides are congruent.
O
B. All obtuse angles are congruent.
O
C. Opposite sides are perpendicular.
O
D. All right angles are congruent.
Answer:look
Step-by-step explanation:
The diagonals of a rectangle exist congruent the necessary conditions are
A. Opposite sides are congruent.
C. Opposite sides are perpendicular.
How to verify that the diagonals of a rectangle are congruent?A quadrilateral exists named a rectangle if the opposite sides exist congruent and parallel to each other. All interior angles exist as right angles and are congruent.
To verify that the diagonals of a rectangle exist congruent the necessary conditions are:
1. Opposite sides of a rectangle exist congruent.
2. All right angles exist congruent.
Therefore, the correct answer is options A and C.
A. Opposite sides are congruent.
C. Opposite sides are perpendicular.
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14 divied by 3/8 equals
Answer:
37 1/3
Step-by-step explanation:
14 divided by 3/8=
14*8/3=
37 1/3
Answer the questions
Answer:
I just know that for number 9.)It's C because it has a greater number, meaning it has a greater chance of containing Adam's house number.
what kind of shape will be this rule on a graph
y= x^2
Answer:
a parabola, sort of like a u shape
Step-by-step explanation:
How many solutions does the following system have?
y=2x-12
y=3x+12
The system has one solution
Step-by-step explanation:
Let us revise the type of the solutions of a system of equations
One solution if the coefficients of x or/and y are different in the simplest form of the two equationsInfinite many solutions if the coefficients of x , y and the numerical terms are equal in the simplest form of the two equationsNo solution if the coefficients of x and y are equal and the numerical terms are different in the simplest form of the two equationsThe system of equations is:
y = 2x - 12 ⇒ (1)
y = 3x + 12 ⇒ (2)
∵ The equations are in its simplest form
∵ The coefficients of x in the two equations are different
- That is the 1st case above
∴ The system has one solution
Let us prove that by solving the system
To solve the system of equations equate (1) and (2) to find x
∵ 3x + 12 = 2x - 12
- Subtract 2x from both sides
∴ x + 12 = -12
- Subtract -12 from both sides
∴ x = -24
- Substitute the value of x in equation (1) or (2) to find y
∵ y = 3(-24) + 12
∴ y = -72 + 12
∴ y = -60
∴ The solution of the system is (-24 , -60)
The system has one solution
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3. The Assistant Principal for Curriculum administered a practice SAT test with 50 questions
to students during an after-school tutoring program. She said a score of 30 or above predicts
a good SAT test score. How many students took the test and how many can expect a good
SAT test score?
O
O
A. 28 students took the test and 14 of them can expect a good SAT test score.
B.28 students took the test and 4 of them can expect a good SAT test score.
C. 28 students took the test and 21 of them can expect a good SAT test score.
D. 26 students took the test and 14 of them can expect a good SAT test score.
OO
O Mark for review (Will be highlighted on the review page)
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Answer:
A
Step-by-step explanation:
Answer:
the answer is c
Step-by-step explanation:
A bag of turf builder sun and shade mix grass seed covers an area of 4000ft.How many bags are needed to cover an area of 35,000ft
Answer: you will get 8.75, but the answer should be 9 bags
Step-by-step explanation:
In the morning, sophie goes to the store the goes to school. In the afternoon she goes from school to her house. The map shows the distance between school and home as 5 cm. If every 4 cm on the scale drawing equals 8 kilometers, how far apart are sophies home and school.
10 km
Step-by-step explanation:
If 4 cm represents 8 kilometers then 1 cm represents;
8 / 4
= 2
1 cm : 2 km
How, then, about 5 cm – the distance between Sophie's home and school?
5 cm : ? km
A cross multiplication;
1 cm : 2 km
5 cm : x km
(5 * 2) = 1 x
x = 10/1
x = 10
simplify this,(p-5)^2-49
Answer:
(p - 12)(p + 2) or
p^2 - 10p - 24.
Step-by-step explanation:
We use the Difference of 2 Squares Identity.
a^2 - b^2 = (a - b)(a + b).
So (p - 5)^2 - 49
= (p - 5 - 7)(p - 5 + 7)
= (p - 12)(p + 2)
= p^2 - 10p - 24.
Answer:
(p - 12)(p + 2)
Step-by-step explanation:
(p-5)² - 49 =
= (p - 5 - 7)(p - 5 + 7)
= (p - 12)(p + 2)
a² - b² = (a - b)(a + b)
a = p - 5
b = 49
complete the equation of the line through (-8, 8) and (1, -10)
Answer:
[tex]y=-2x-8[/tex]
Step-by-step explanation:
Let [tex]y=mx+c[/tex] be the equation of this line.
The points must satisfy this equation.
When x=-8, and y=8, we get:
[tex]8=-8m+c....(1)[/tex]
When x=1, and y=-10, we get:
[tex]-10=m+c...(2)[/tex]
Subtract equation (1) from equation (2) to get:
[tex]m--8m=-10-8[/tex]
9m=-18
m=-2
We put m=-2 in equation to get (2)
-10=-2+c
c=-10+2
c=-8
Therefore the equation is:
y=-2x-8
The 1984 movie footloose made $8,556,965 in its opening weekend. The 2011 remake of footloose made $15,556,113 in its opening weekend. What is the absolute and relative change in opening weekend earnings from the original footloose to its remake? Round your answer for relative change to the nearest hundreth of a percent. Do not round until your final answer.
Answer:
absolute change: $6,999,148relative change: 81.79%Step-by-step explanation:
The absolute change is the difference between the earnings numbers:
$15,556,113 -8,556,965 = $6,999,148
__
The relative change is the ratio of this difference to the original amount:
$6,999,148/$8,556,965 × 100% ≈ 81.794748% ≈ 81.79%
The absolute change in opening weekend earnings from the original Footloose to its remake is $6,999,148, and the relative change is approximately 81.74%.
Explanation:To calculate the absolute change in opening weekend earnings from the original Footloose movie to its 2011 remake, we subtract the earnings of the original movie from the earnings of the remake. Thus, the absolute change is $15,556,113 - $8,556,965 = $6,999,148.
To find the relative change, we divide the absolute change by the original amount and then multiply by 100 to get a percentage. This gives us ($6,999,148 / $8,556,965) * 100 ≈ 81.74%. Hence, the relative change is approximately 81.74%.
The absolute change represents the direct increase in dollar amount, while the relative change gives us the percentage increase from the original to the remake's opening weekend earnings, providing insight into the growth rate.
The ratio of people to books in a classroom is 10:4 what is the unit rate of people per book
Answer:
Unit rate of people per book = 2.5
Step by step explanation:
Given:
Number of peoples = [tex]10[/tex]
Number of books = [tex]4[/tex]
Their ratios = [tex]10 : 4[/tex]
We have to find the unit rate of people per book.
To find out the unit rate of people per book we have to divide the total number of peoples by the total number of books.
Or
For this we will follow the unitary method:
For [tex]4[/tex] book there are [tex]10[/tex] persons.
For [tex]1[/tex] book there will be [tex]\frac{10}{4}[/tex] persons.
So,
The numeric value = [tex]\frac{10}{4}[/tex]
= [tex]2.5[/tex]
There are 2.5 people per book and that it also the unit rate of people per book.
Tom drinks 8oz of water for every 3 miles he bikes after 21 miles how much water did he drink
Answer:
he drinks 56oz of water
Step-by-step explanation:
divide 21 by 3 that would equal seven than multiply it by 8 which is 56
Answer:
57 ounces
Step-by-step explanation:
[tex]\frac{3 miles}{8oz water}[/tex] × 7 = [tex]\frac{21miles}{56ozwater}[/tex]
Can you show the work for (4x-4)(x-4)
Answer:
4x² - 20x + 16
Step-by-step explanation:
Given
(4x - 4)(x - 4)
Each term in the second factor is multiplied by each term in the first factor, that is
4x(x - 4) - 4(x - 4) ← distribute both parenthesis
= 4x² - 16x - 4x + 16 ← collect like terms
= 4x² - 20x + 16
Which statements are true? Check all that apply. StartRoot 1.8 EndRoot < 1.8 StartRoot 1.8 EndRoot greater-than 1 StartRoot 1.8 EndRoot less-than StartRoot 1.9 EndRoot 1.3 less-than StartRoot 1.8 EndRoot less-than 1.4 StartRoot 1.9 EndRoot + StartRoot 1.8 EndRoot greater-than 2 StartRoot 1.9 EndRoot minus StartRoot 1.8 EndRoot greater-than 0.1
The first, second, third, and fifth statements are true, but the fourth and sixth statements are false. The responses are based on evaluating the square root calculations.
Explanation:The statements we are analyzing are related to the square root of 1.8 (√1.8). Let's work through them:
√1.8 less than 1.8: This statement is true because the square root of a positive number less than its actual number.√1.8 greater than 1: This is true. Since √1.8 is approximately 1.34, which is greater than 1.√1.8 less than √1.9: This is true. Since the larger the number, the larger its square root will be.1.3 less than √1.8 less than 1.4: This is false. As previously stated, √1.8 is approximately 1.34, so it's not less than 1.3 nor greater than 1.4.√1.9 + √1.8 greater than 2: This is true. √1.9 is approximately 1.38 and √1.8 is 1.34. Adding these values exceeds 2.√1.9 − √1.8 greater than 0.1: This is false. The difference between √1.9 and √1.8 is less than 0.1.Learn more about Square Root Comparisons here:https://brainly.com/question/30877013
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Me Matthews purchases 22 boxes of pencils for 5 fourth grade classes. Each box contains 45 pencils. How many pencils will each class receive?
Answer: 198 pencils per class
Explanation:
22 boxes * 45 pencils = 990 pencils
990 pencils / 5 classes = 198 pencils per class
Answer: 198 pencils per class
Explanation:
22 boxes * 45 pencils = 990 pencils
990 pencils / 5 classes = 198 pencils per class
.
The measures of the angles of triangle RST are in the ratio 2:4:9. What are the measures of the angles ?
Measures of the angles are 24°, 48° and 108°
Step-by-step explanation:
Step 1: Given ratio = 2:4:9. Sum of angles of triangle = 180°Let angles be 2x, 4x and 9x.
⇒ 2x + 4x + 9x = 180
⇒ 15x = 180
⇒ x = 180/15 = 12
Step 2: Find angles.2x = 24°, 4x = 48° and 9x = 108°
What is the rate of change of the function described in the table?
the average rate of change of the function over the interval [tex]\(10 < x < 15\)[/tex] is [tex]\( -\frac{6}{5} \)[/tex].
To find the average rate of change of the function over the interval (10 < x < 15), we use the formula:
[tex]\[ \text{Average Rate of Change} = \frac{\text{Change in } f(x)}{\text{Change in } x} \][/tex]
We can calculate the change in [tex]\(f(x)\)[/tex] by subtracting the function values at the end and start of the interval, and the change in x by subtracting the end and start values of x.
Given the function values:
- [tex]\(f(10) = 30\)[/tex]
- [tex]\(f(15) = 24\)[/tex]
And the interval [tex]\(10 < x < 15\)[/tex], the change in [tex]\(f(x)\) is \(f(15) - f(10) = 24 - 30 = -6\)[/tex].
The change in x is [tex]\(15 - 10 = 5\)[/tex].
Now, we plug these values into the formula for the average rate of change:
[tex]\[ \text{Average Rate of Change} = \frac{-6}{5} \][/tex]
So, the average rate of change of the function over the interval [tex]\(10 < x < 15\)[/tex] is [tex]\( -\frac{6}{5} \)[/tex].
The complete Question is given below:
Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 10 < x < 15
x | f(0)
0 | 42
5 | 36
10 | 30
15 | 24
20 | 18
25 | 12
the ratio of girls to boys in a gym class is 1 to 2 if there are 30 students in the class how many girls are in the class?
Answer:
10 Girls
Step-by-step explanation:
This shows that there is twice as many boys in the gym class than girls.
Step 1: Determine what the ratio relates to the amount
1:2 -> 10:20
10 Girls
20 Boys
Answer:
The enswer is corect because is the biggest then girls to boys
Step-by-step explanation:
Please help
Find the volume for each individual shape
Find the composite volume of the original figure.
Answer:
92.11 cm³
Step-by-step explanation:
The figure below;
Has two hemispheres, and An open cylinder The radius of the hemisphere is 2 mmThe height of the cylinder is 6 mm (10 mm - 4 mm)We are required to determine the volume of the figure;
The volume of a hemisphere is given by;
Volume hemisphere = 2/3πr³
Taking π to be 3.14
The Volume of the two hemisphere;
= 2/3 × 3.14 × 2³
= 16.75 cm³
Volume of the cylinder;
Volume = πr²h
= 3.14 × 2² × 6
= 75.36 cm³
Thus, volume of the figure;
= 16.75 cm³ + 75.36 cm³
= 92.11 cm³
Hence, the volume of the figure is 92.11 cm³
you earned 139.20 in simple interest off of 1450 investment in 8 years. What is your annual percentage rate?(Expressed as a percent)
The annual percentage rate is: 1.2%
Step-by-step explanation:
The formula for calculating simple interest is:
[tex]I = Prt[/tex]
Here
P is the principal amount
r is the interest rate
t is the time in years
We are Given:
[tex]P = 1450\\t = 8\ years\\I = 139.20[/tex]
Putting the values in the formula
[tex]139.20 = 1450 * r * 8\\139.20 = 11600r[/tex]
Dividing both sides by 11600
[tex]\frac{11600r}{11600} = \frac{139.20}{11600}\\r = 0.012[/tex]
Converting into percentage
r = 0.012*100
r = 1.2%
Hence,
The annual percentage rate is: 1.2%
Keywords: Percentage, interest
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What is nine - fifteenths minus two - sixths
Answer: four-fifteenths or [tex]\frac{4}{15}[/tex]
Step-by-step explanation:
What is written with words is mathematically expressed as:
[tex]\frac{9}{15}-\frac{2}{6}[/tex]
We can simplify both fractions, by dividing the numerator and denominator of the first by 3 and dividing the numerator and denominator of the second by 2:
[tex]\frac{9}{15}=\frac{3}{5}[/tex]
[tex]\frac{2}{6}=\frac{1}{3}[/tex]
Then:
[tex]\frac{3}{5}-\frac{1}{3}[/tex]
Calculating the least common multiple (l.c.m) in the denominator as [tex]15[/tex]:
[tex]\frac{9-5}{15}=\frac{4}{15}[/tex] This is the result: four-fifteenths
How do I do this????????????
Answer:
10 rows with the set of 100 blocks is what she will make
Step-by-step explanation:
Where
First row is 1
Second row is 3
Third row is 5
This shows that the blocks are set in an oddly fashion
Meaning each row has a odd number of blocks
Therefore from
1 block- row 1
3 blocks- row2
5 blocks- row 3
7 blocks - row 4
9 blocks- row 5
11 blocks - row 6
13 blocks- row 7
15 blocks - row 8
17 blocks- row 9
19 blocks - row 10
Add of the blocks it amounts to 100 blocks
Meaning the triangular will be at the 10th row when she has use 100 blocks
When 15 is subtracted from 3 times a number the result is -32. what is the number?
Answer:
15.6
Step-by-step explanation:
15+32=47
47/3=15.6
since the - is there
it will be -15.6
Answer:
Step-by-step explanation:
let x represent the number
3x - 15 = -32
3x = -32 + 15
3x = -17
x = -17/3 or - 5 2/3 <====
Function 1: y = 4x + 5 Function 2: The line passing through the points (1, 6) and (3, 10). Which of these functions has the greater rate of change? A) Function 1, because the slope is 5 and the slope of function 2 is 4. B) Function 1, because the slope is 4 and the slope of function 2 is 2. C) Function 2, because the slope is 7 and the slope of function 1 is 5. D) Function 2, because the slope is 5 and the slope of function 1 is 4. Eliminat
Answer:
Step-by-step explanation:
function 1 : y = 4x + 5
In y = mx + b form, which is what ur equation is in, the slope can be found in the m position. So the slope of this function is 4.
function 2 : (1,6),(3,10)
slope = (y2 - y1) / (x2 - x1)
(1,6)...x1 = 1 and y1 = 6
(3,10)...x2 = 3 and y2 = 10
now we sub
slope = (10 - 6) / (3 - 1) = 4/2 = 2
B. Function 1, because the slope is 4 and the slope of function 2 is 2. <==
Answer:
Function 1, because the slope is 4 and the slope of function 2 is 2. Use the slope formula.