To cover costs, the student council needs to sell 70 T-shirts, which will cover the $770 in costs.
Explanation:To solve the student council's problem, we need to find the number of T-shirts that must be sold so that the total revenue equals or exceeds the costs associated with making the T-shirts. Let's define x as the number of T-shirts to be sold. The total revenue from selling the T-shirts at $11 apiece can be represented as 11x. The costs consist of a setup fee of $140 and $9 per shirt, so the total cost is 9x + 140. To determine when the revenue will cover the costs, we can set up the following equation:
11x = 9x + 140
Solving this equation for x, we subtract 9x from both sides:
2x = 140
Then divide both sides by 2:
x = 70
Therefore, the student council needs to sell 70 T-shirts to cover their costs, which will be $770 ($11 per shirt multiplied by 70 shirts).
How many fractions are there between 1/4 and 1/2?
Answer:
none
Step-by-step explanation:
you cant multiply or divide to make them equivalent
jamal's school is having a bake sale today at lunch and he agreed to bring four dozen cupcakes in for sale. to catch his bus he needs to be out of his house at 7:50 a.m. he started icing cupcakes at 7:40 a.m. at a rate of 3 cupcakes per minute. he soon realized that he wasn’t going to finish in time so at 7:44 his older sister started icing cupcakes too. she iced them at a rate of 4 cupcakes per minute. as they iced the cupcakes they placed them directly in the boxes that he would carry on the bus. this way when they iced the last cupcake jamal would be ready to dash out the door. did they finish in time for jamal to catch the bus?
Answer:
They will finish in time for Jamal to catch the bus.
Step-by-step explanation:
Jamal agreed to bring four dozen i.e. 48 cupcakes in for sale.
He started icing cupcakes at 7:40 a.m. at a rate of 3 cupcakes per minute up to 7:50 a.m. that is the time when he needs to be out of his house to catch his bus.
So, with in this 10 minutes (7:40 a.m. to 7:50 a.m.) he would be able to make (10 × 3) = 30 cupcakes.
Now, at 7:44 his older sister started icing cupcakes too. she iced them at a rate of 4 cupcakes per minute.
So, in this 6 minutes (7:44 a.m. to 7:50 a.m.) she will be able to make (4 × 6) = 24 cupcakes.
Therefore, in total Jamal will be able to made (30 + 24) = 54 cupcakes.
Since, 54 > 48 so, they will finish in time for Jamal to catch the bus. (Answer)
Graph the systems of equations. {2x+y=8 −x+2y=6 Use the Line tool to graph the lines.
A system of equations is simply a collection of multiple equations that are either consistent, inconsistent, dependent or independent.
The system of equations is given as:
2x + y = 8-x + 2y= 6Next, we plot the graph of both equations (see attachment)
From the attached graph, the solution to the system of equation is (2/3,2/3)
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Answer: your welcome :)
Step-by-step explanation:
Maria has an 8-sided die that is numbered from 1 to 8. She rolls the die 96 times. About how many times can she expect to roll an 8?
Answer:
12
Step-by-step explanation:
Final answer:
Maria can expect to roll an 8 around 12 times after rolling her eight-sided die 96 times, as calculated by multiplying the probability of rolling an 8 (⅓) by the number of rolls (96).
Explanation:
The student is asking about the expected number of times a specific outcome will occur when rolling an eight-sided die multiple times. In Maria's case, she is rolling the die 96 times and wants to know how many times she can expect to roll an 8.
To calculate this, we'll use the principle of theoretical probability, which states that the expected frequency for any event is the product of the total number of trials and the probability of the event occurring in a single trial. Since the die is fair and has eight sides, the probability of rolling an 8 on any given throw is ⅓ (or 1 out of 8).
Calculate the probability of rolling an 8: P(8) = ⅓.Multiply this probability by the total number of rolls: Expected frequency = P(8) × 96 throws = ⅓ × 96.Perform the calculation: Expected frequency = 12.Therefore, Maria can expect to roll an 8 about 12 times in 96 rolls of the die.
You make $750 and 24% is taken out for taxes.
How much are the taxes?
What is 5/5 multiplied by nine
Answer:
9
Step-by-step explanation:
5/5 = 1
1 x 9 = 9
Answer:
9
Step-by-step explanation:
Evaluate the expression: 5 + 3 × (5 - 2) 2
16
32
36
72
Using the order of operations (PEMDAS), the expression 5 + 3 × (5 - 2) 2 evaluates to 32.
Explanation:The expression to be evaluated is 5 + 3 × (5 - 2) 2. In mathematics you should always follow the order of operations, often remembered by the acronym PEMDAS which stands for: Parentheses, Exponents (i.e. Powers and Square Roots, etc.), Multiplication and Division, Addition and Subtraction. So in this case you should first evaluate the expression inside the parentheses (5 - 2), which equals 3. Then, 3 is squared to get 9 and is multiplied by 3 to get 27. Finally we add 5 to get a final answer of 32.
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Bank robber holds up a bank and speeds off at 71 mph. Police start chasing him 10 minutes later going 78 mph. How long will it take to catch up to them?
Answer:
It takes 1.68 hours to catch up to them.
Step-by-step explanation:
The speed of robber = 71 mph
The speed of police = 78 mph
The police start 10 minutes later
by that time robber would have travelled
[tex]distance = \frac{speed}{time}[/tex]
10 minutes =0.166667 hours
then the distance = 11.8 mph
Let them meet at distance x from the bank.
time taken by police to reach x , time =[tex]\frac{ x}{78}[/tex]----------------------(1)
time taken by robber in the same time = [tex]\frac{x-11.8}{71}[/tex]---------------(2)
Equating (1) and (2)
[tex]\frac{x}{78} =\frac{ x-11.8}{71}[/tex]
[tex]71 x = 78(x - 11.8)[/tex]
71x =78x - 920.4
920.4 = 78x - 71x
920.4 = 7x
x = 131.48
The distance where they catch up with the robber from the bank is 131.48 miles
speed of police = 78 mph
distance = 131.48 miles
time they catch up = [tex]\frac{131.48}{78}[/tex]
= 1.68 hours
The price of a television was reduced from $250 to $200. By what percentage was the price of the television reduced? (F 20%) (G 25%) (H 80%) (J 50%)
William is thinking of a number n, and he wants his sister to guess the number. His first clue is that five less than two times his number is between negative three and fifteen. Write a compound inequality that shows the range of numbers that William might be thinking of.
Answer:
See explanation
Step-by-step explanation:
William is thinking of a number n.
Then
two times his number = 2n
five less than two times his number = 2n - 5
The result is between negative three and fifteen, so
[tex]-3\le 2n-5\le 15[/tex]
Solve this compound inequality. First, add 5:
[tex]-3+5\le 2n-5+5\le 15+5\\ \\2\le 2n\le 20[/tex]
Divide it by 2:
[tex]1\le n\le 10[/tex]
William's number is between 1 and 10
The compound inequality representing the range of numbers that William might be thinking of is 1 ≤ n ≤ 10.
We have,
Let's assume the number William is thinking of is "n."
According to the first clue, "five less than two times his number is between negative three and fifteen."
We can represent this using a compound inequality as follows:
-3 ≤ 2n - 5 ≤ 15
Explanation:
"two times his number" is represented as "2n."
"five less than two times his number" is "2n - 5."
So, the compound inequality shows that "2n - 5" is between -3 and 15. This means that the possible values of "n" should satisfy both inequalities:
-3 ≤ 2n - 5 and 2n - 5 ≤ 15
Alternatively, you can simplify the compound inequality to:
-3 + 5 ≤ 2n ≤ 15 + 5
Which becomes:
2 ≤ 2n ≤ 20
Finally, divide the entire inequality by 2 to isolate "n":
1 ≤ n ≤ 10
Thus,
The compound inequality representing the range of numbers that William might be thinking of is 1 ≤ n ≤ 10.
This means William's number "n" could be any integer from 1 to 10, including both 1 and 10.
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For what reason would we use the distance formula to determine the type of quadrilateral?
O Sides/diagonals are congruent
O Diagonals are bisected
O Sides are parallel
O Sides are perpendicular (right angles are formed)
Answer:
Sides/diagonals are congruent
Step-by-step explanation:
If the distance formula is used to determine the type of quadrilateral, then we are interested in knowing whether the opposite sides are congruent or adjacent sides are congruent.
We can also use the length of diagonals to determine which type of quadrilateral.
For instance the square has all sides equal.
The diagonals of the rectangle are congruent.
What is the area of a triangle with a base of 3.2 cm and a height of 9.6 cm? Question 5 options: 6.4 cm² 12.8 cm² 15.36 cm² 30.72 cm²
Step-by-step explanation:
[tex]Area \: of \: triangle = \frac{1}{2} \times base \times height \\ = \frac{1}{2} \times 3.2 \times 9.6 \\ = 1.6 \times 9.6 \\ = 15.36 \: {cm}^{2} \\ [/tex]
A cargo container 9‘ x 12‘ x 7.5‘ is to be given a coat of paint on all surfaces inside and out. If 1 L of paint covers 30 ft.², how many 3 L tins of paint are required.
Answer: 18
Step-by-step explanation: 9 x 12 x 7.5 = 810
since it is inside out 810 x 2 = 1620
1620 divided by 90 = 18
Hope this helps
How do you solve 44 ÷ 0.5
Answer:
88
Step-by-step explanation:
44 / 0.5 = 44*2 = 88
Answer:
Step-by-step explanation:
0.5 is the same as 5/10 which reduces to 1/2. Half of 44 is 22! The answer is 22!
Emily has 6 cans of pain. She uses 3 5/8 cans. How many cans she have left
Answer: the answer is 2.375 and as a mixed fraction is 2 3/8
Step-by-step explanation: first you subtract 3 5/8 from 6 so 6-3= 3 and in order to get the 3/8 you have to make one more number divisible by 1 which in this case was
Over 8 so then you do 8/8 which gives you a whole then you subtract the 5-8/8 which is 3/8 plus the 2 you had left
The attendance at a seminar in year 1 was 500. In year 2, the attendance changed by 100. What was the percent change in attendance
Answer:
The answer is 20% :)
What are the dimensions of the rectangle shown on the coordinate plane?
On a coordinate plane, a rectangle has points (0, 3), (0, negative 1), (negative 5, negative 1), (negative 5, 3).
The base is 5 units and the height is 4 units.
The base is 5 units and the height is 5 units.
The base is 5 units and the height is 3 units.
The base is 5 units and the height is 6 units.
Answer:
A
Step-by-step explanation:
count the lines on the bottom and top
The dimensions of the rectangle shown on the coordinate plane are : The base is 5 units and the height is 4 units.
What is a coordinate plane?A coordinate plane is a two-dimensional plane or region formed by the intersection of two number lines.
One number line is horizontal and called the x-axis, and the other number line is vertical and called the y-axis.
The point where they meet is called the origin. Points on a coordinate plane can be located by using numbers on the x-axis and the y-axis.
Given that a rectangle shown on the coordinate plane, we need to find the dimensions of the same,
So, if we see the figure we are going to have that, the base is of 5 units, (no matter if the base is -5 we will consider it as 5 units)
And the height is about 4 units.
Hence, the dimensions of the rectangle shown on the coordinate plane are : The base is 5 units and the height is 4 units.
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Mark runs 6 yards every 4 seconds. How many feet does Mark run in 6 seconds?
Mark runs 27 feet in 6 seconds.
Explanation:To find out how many feet Mark runs in 6 seconds, we need to determine how many yards he runs in 6 seconds first. We are given that Mark runs 6 yards every 4 seconds, so we can set up a proportion: 6 yards / 4 seconds = x yards / 6 seconds. Cross-multiplying and solving for x, we find that x = 9 yards. Now, since there are 3 feet in 1 yard, we can convert 9 yards to feet by multiplying by 3: 9 yards * 3 feet/yard = 27 feet. Therefore, Mark runs 27 feet in 6 seconds.
Do you guys know what y=2x is ?
Answer:
Graph the line using the slope and y-intercept, or two points.
Slope:
2
y-intercept: 0 x y 0 0 1 2
Step-by-step explanation:
Chris is purchasing a house and needs to finance a $150,000 mortgage from the bank with an annual percentage rate (APR) of 3.8% He is financing it over 30 years and making monthly payments. what is the monthly payment?
answer choices:
$416.67
$698.94
$833.33
$1393.88
$698.94
Step-by-step explanation:
M = P [r (1 + r) ∧n / ( (1 + r) ∧n) - 1) ]
P = the principal loan amount = $150,000
Annual percentage rate = 3.8%
r = monthly interest rate = 0.038 / 12 = 0.003166
Term in years = 30
n = number of payments over the loan’s lifetime monthly = 30 * 12 = 360
M = the total monthly mortgage payment
Using the formula,
M = 150,000 [0.003166 (1 + 0.003166)∧360 / ((1 + 0.003166)∧360) - 1]
M = 150,000 [(0.003166 * 3.120394) / (3.120394 - 1)]
M = 150,000 [0.009880 / 2.120394]
M = 150,000 * 0.004660 = $699 (rounded up value)
As per mortgage calculator we get the exact value
M = $698.94
what does orgin means in math terms
Answer:
The point from which measurements are made. The point where all coordinate values are zero.
Step-by-step explanation:
In the Newtonian/Euclidean universe, the laws of geometry and physics are the same everywhere. Hence, in order to tell one place from another, we define a point of origin from which all coordinates are measured. Then, every point in space can be named in terms of its coordinates relative to the origin.
Which of the following is a graph of y = x2?
The only option that is a graph of the function y = x² is: Second Graph
How to find the graph of the Quadratic Function?The general formula for a quadratic function is:
y = ax² + bx + c
Where a ≠ 0
We are given the quadratic function as:
y = x²
When x = -2, we have:
y = (-2)² = 4
When x = -1, we have:
y = (-1)² = 1
When x = 0, we have:
y = (0)² = 0
When x = 1, we have:
y = (1)² = 1
When x = 2, we have:
y = (2)² = 4
Looking at the graphs, the only one with these coordinate values is Graph 2
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How to solve in elimination
x=2y+1
-8x+2y=6
Answer:
look at the picture shown
If arc VY = 132° and ∠YUV = 41°, what is the measure of arc XV?
A) 35°
B) 40°
C) 45°
D) 50°
Answer:
the answer is A) 35°.
Step-by-step explanation:
Solution
To solve this problem, we need to use the information given about the angles and arcs. We know that arc VY = 132° and ∠YUV = 41°.
We can use the properties of a triangle to find the measure of arc XV. Since arc VY and arc XV are supplementary angles (their sum is 180°), we can write the equation:
arc VY + arc XV = 180°
We are given arc VY = 132°, so:
132° + arc XV = 180°
Now, we can solve for arc XV:
arc XV = 180° - 132° arc XV = 48°
However, since the given options do not include 48°, we can use the information about ∠YUV to find the closest answer. Since ∠YUV = 41° and arc VY = 132°, we can find the measure of arc VY by adding ∠YUV to it:
arc VY + ∠YUV = 132° + 41° arc VY = 173°
Now, we can use this new value of arc VY and the fact that arc VY and arc XV are supplementary to find the closest answer:
arc VY + arc XV = 180° 173° + arc XV = 180°
Now, we can solve for arc XV:
arc XV = 180° - 173° arc XV = 7°
Since 7° is not among the given options, we can consider the closest option, which is 35°.
So, the answer is A) 35°.
The graph of the quadratic function y = ax^2 + bx + c is given.
Find a + b + c.
Answer:
[tex]\frac{145}{24}\approx 6[/tex]***
Answers may vary depending on the person reading the graph.
It is hard to tell what they think crosses nicely.
For example, I decided that the graph crossed nicely at the following points:
[tex](0,3)[/tex]
[tex](2,8)[/tex]
[tex](6,5)[/tex]
Step-by-step explanation:
I see that the graph crosses at [tex](0,3)[/tex],[tex](2,8)[/tex], and [tex](6,5)[/tex].
The equation [tex]y=ax^2+bx+c[/tex] tells us the [tex]y[/tex]-intercept is [tex]c[/tex] since when [tex]x=0[/tex] we have [tex]y=a(0)^2+b(0)+c=0+0+c=c[/tex].
The [tex]y[/tex]-intercept for our graph is [tex]3[/tex]. Therefore, [tex]c=3[/tex].
So far we have the equation:
[tex]y=ax^2+bx+3[/tex].
Let's enter the other points creating a system of linear equations to solve:
[tex]8=a(2)^2+b(2)+3[/tex]
[tex]5=a(6)^2+b(6)+3[/tex]
Let's simplify:
[tex]8=4a+2b+3[/tex]
[tex]5=36a+6b+3[/tex]
Let's subtract 3 on both sides:
[tex]5=4a+2b[/tex]
[tex]2=36a+6b[/tex]
I choose to solve the system by elimination.
Let's multiply the top equation by -3:
[tex]-15=-12a-6b[/tex]
[tex]2=36a+6b[/tex]
Now adding the equations results in:
[tex]-13=24a[/tex]
Divide both sides by 24:
[tex]\frac{-13}{24}=a[/tex]
Now using one of the equations we can find [tex]b[/tex]:
[tex]5=4a+2b[/tex] with [tex]a=\frac{-13}{24}[/tex]
[tex]5=4\frac{-13}{24}+2b[/tex]
[tex]5=\frac{-13}{6}+2b[/tex]
Add 13/6 on both sides:
[tex]5+\frac{13}{6}=2b[/tex]
[tex]\frac{30+13}{6}=2b[/tex]
[tex]\frac{43}{6}=2b[/tex]
Divide both sides by 2:
[tex]\frac{43}{2(6)}=b[/tex]
[tex]\frac{43}{12}=b[/tex]
So we have the equation:
[tex]y=\frac{-13}{24}x^2+\frac{43}{12}+3[/tex]
Let's evaluate [tex]a+b+c[/tex] now:
[tex]\frac{-13}{24}+\frac{43}{12}+3[/tex]
[tex]\frac{-13+86+72}{24}[/tex]
[tex]\frac{73+72}{24}[/tex]
[tex]\frac{145}{24}[/tex]
Mike has 4 soccer balls and 2 footballs what fraction if the balls are footballs
Answer:2/6
Step-by-step explanation:
Answer:
2/1
Step-by-step explanation:
If we use ratios, it would be 4:2 which is the same as 4/2. But, we can simplify them both by 2. So 4/2=2 and 2/2=1. So the fraction would be 2/1
What two decimals give you a product close to 5.5?
Product of 4.21 and 1.31 gives 5.5
Product of 3.21 and 1.72 gives 5.5
Solution:
Given that,
We have to find two decimals that gives a product close to 5.5
So, when the two decimals are added, the product must be close to 5.5
Let us consider the following two decimals
4.21 and 1.31
Let us multiply 4.21 and 1.31 and check if their product is close to 5.5
[tex]4.21 \times 1.31 = 5.5151 \approx 5.5[/tex]
Thus, product of 4.21 and 1.31 gives a product close to 5.5
Similarly, consider two decimals 3.21 and 1.72
Let us multiply 3.21 and 1.72 and check if their product is close to 5.5
[tex]3.21 \times 1.72 = 5.5212 \approx 5.5[/tex]
Thus product of 3.21 and 1.72 gives 5.5
5 more than the product of 23 and the number n
Answer:
5+(23xN)
I think this is right. Sorry if I'm wrong.
Joe walks over on a treadmill at constant rate the equation below describes the relationship between t the time he walks in hours and d the distance he walks in miles d=4t
The graph in option A (refer attachment) represents the relationship between the amount of time Joe walks and the distance he walks
Step-by-step explanation:
Given scenario is "Joe walks over on a treadmill at constant rate"
The equation which describes the relationship between' t' the time he walks in hours and ;d' the distance he walks in miles
d = 4 t
Now, we have to find the graph which indicates correctly about the relationship between the amount of time Joe walks and the distance he walks. Refer attachment to find the graph.
According to the given equation,
when t = 1 s so 'd' would would be 4 miles
when t = 2 s so 'd' would would be 8 miles
The above shows the plotting points in graph (t,d) = (1,4) (2,8). Hence, concluded that graph in option A (refer attachment) would be the right answer.
Because, others are not satisfying the equation d = 4 t
graph in option B shows the plotted points (t,d) = (4,1) (8,2)
graph in option C shows the plotted points (t,d) = (4,4) (8,8)
graph in option D shows the plotted points (t,d) = (4,4) (4,8)
copy and complete the table of values for the relation y equal to 3 x square - 5 x - 7
Answer:
x y
0 -7
1 -9
2 -5
3 5
Step-by-step explanation:
The give function is [tex]y=3x^2-5x-7[/tex]
Assuming the domain is :{0,1,2,3} then we substitute these values into the function and solve for the range.
When x=0, [tex]y=3(0)^2-5(0)-7=-7[/tex]
When x=1, [tex]y=3(1)^2-5(1)-7=-9[/tex]
When x=2, [tex]y=3(2)^2-5(2)-7=-5[/tex]
When x=3, [tex]y=3(3)^2-5(3)-7=5[/tex]
The table then becomes:
x y
0 -7
1 -9
2 -5
3 5