A marching band director needs to divide 44 members into two groups. He wants the ratio of band members in group 1 to band members in group 2 to be 1 to 3. How many band members will be in group 2?.
If the ratio of band members in group 1 to band members in group 2 is 1 to 3, then for every 3 band members in group 2, there will be 1 band member in group 1.Therefore, group 2 will have 11 band members.
What is ratio and proportion?Comparing two numbers or quantities results in a ratio. Usually, it is expressed in the form "a:b" or "a/b," with a and b standing for the two quantities under comparison. Contrarily, a percentage is an equation that states that two ratios are equal. Alternatively said, a proportion is a claim that one ratio is equal to another.
For example, if the ratio of apples to oranges in a basket is 2:3, this implies that there are three oranges per each two apples. We may alternatively state that the ratio of apples to total number of fruits in the basket is 2:5, because 2 + 3 = 5. The two ratios (2:3 and 2:5) are proportionate in this instance. Also, ratio of band members in group 1 to band members in group 2 to be 1 to 3
How to solve?
If the director wants to divide 44 band members into two groups, with this ratio, then the number of band members in group 2 will be 44 / (1 + 3) = 44 / 4 = 11 band members.
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A total of 420 tickets were sold for the school play they were either adult tickets or student tickets the number of student tickets sold was three times the number of adult tickets sold how many adult tickets were sold
Answer: I believe 140
Step-by-step explanation: This is how I found my answer:
420 / 3
= 140
420-140
= 280
420= number of all tickets sold.
140= number of adult tickets sold
280= number of student tickets sold
You might wonder how I know why it's 140. I know it's 140, because using my context clues, it stated:
"the number of student tickets sold was three times the number of adult tickets."
So, the one that was the bigger amount must be the student's tickets sold, while the lower amount has to be the adult's tickets sold. I hope this helped!
Paige can sort her toys in 6 fewer hours that Madison can. When they work together, it
takes them only 4 hours to sort the toys. How long would it take for each of them to sort
the toys alone?
Let X be the number of hours it takes Paige to sort the toys alone.
It takes Madison X + 6 hours to sort the toys alone.
Together, it takes them X + (X + 6) = 4 hours to sort the toys.
Combining like terms, we get 2X = 4
Dividing both sides by 2, we get X = 2
Therefore, it takes Paige 2 hours to sort the toys alone.
It takes Madison 2 + 6 = 8 hours to sort the toys alone.
Determine the slope of m of the line in the graph below
Please help me
Answer:
Step-by-step explanation:
(2, 0), (3, 4)
(4 - 0)/(3 - 2)= 4/1 = 4
innequality of |2x+7|+9 >18.
For the given inequality of |2x+7|+9 >18 the values of x are x< -8 or x>1.
What is meant by inequality?The state of not being equal, particularly in terms of status, rights, and opportunities, is a fundamental concept in social justice theories. It can be perplexing in public conversation since it typically has distinct meanings to different individuals. However, some variations are common. An inequality in mathematics is a comparison between two numbers or other mathematical expressions that is unfair. Various notations are used to denote different kinds of inequality, including:
A less than sign, such as a, denotes that an is greater than b.
Given inequality is:
|2x+7|+9 >18.
First we have to rearrange all the variables to the left side of the given equation:
Then,
|2x+7|>18-9
|2x+7|>9
2x+7>9 or 2x+7< -9
S0, x>1 or x< -8
Therefore, x< -8 or x>1
Hence, For the given inequality of |2x+7|+9 >18 the values of x are x< -8 or x>1.
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Find the area of the triangle below. Be sure to include the correct unit in your answer. 8 cm 9 cm 18 cm
Answer:
648
Step-by-step explanation:
An easy way to do this is to multiply all sides, then divide by 2.
8 × 9 × 18 = 1296
Now divide that by 2:
1296 ÷ 2 = 648
The area of the triangle is 648.
-2x2 + 8x = 10 using the Quadratic Formula. Simplify if possible.
The required solutions are x = 2-i and x = 2+i to the given quadratic function.
What is a quadratic function?
The quadratic function is defined as a function containing the highest power of a variable is two.
We have been given that quadratic function as
-2x² + 8x - 10 = 0
Compare the given function to the standard quadratic function f(x) = ax² + b x + c.
We get a = -2, b = 8 and c = -10
Using the quadratic formula to solve the above quadratic function
[tex]x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\dfrac{-8\pm \sqrt{8^2-4\left(-2\right)\left(-10\right)}}{2\left(-2\right)}[/tex]
[tex]x=\dfrac{-8\pm \:4i}{2\left(-2\right)}[/tex]
[tex]x=\dfrac{-8+4i}{2\left(-2\right)},\:x=\dfrac{-8-4i}{2\left(-2\right)}[/tex]
x = 2-i, x = 2+i
Thus, the required solutions are x = 2-i and x = 2+i to the given quadratic function.
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Write an equation in slope-intercept form of the line that is perpendicular to the one given and passes through the given point. (4,8); y=-2x - 4
answer:
step by step explanation:
(4,8); y = 2x — 4 = ?
TO FIND THE ANSWER TO YOUR QUESTION:What is the slope of the line that passes through the points (10, 3)(10,3) and (7, 0)(7,0)? write your answer in simplest form.
The slope of the line that passes through the points (10, 3)(10,3) and (7, 0)(7,0)= 1.
What is slope?A line's steepness and direction are measured by the line's slope.
Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
Any two different points on a line can be used to calculate the slope of any line.
A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively.
Two locations located on a straight line can be used to determine a line's slope. We can use the slope of line formula if we know the two spots' coordinates. These two points' coordinates should be-
P1 = (x1, y1) and P2 = (x2, y2)
According to our question-
The slope m using the slope formula
m = y2-y1/x2-x1
with (x₁, y₁ ) = (10, 3 ) and (x₂, y₂ ) = (7, 0 )
-3/-3 = 1
Hence, the slope is = 1.
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1/2 divided by 2 In fraction
Answer:
1/4
Step-by-step explanation:
1/2 divided by 2 would be 0.25, and since that's a quarter it would be 1/4.
A quare i drawn on a grid. Two of it vertice are at (3,3) and (7,7) What i the perimeter of the quare?
Therefore the solution of this question is the perimeter of the square on the grid is 16[tex]\sqrt{2}[/tex] units
What is perimeter?A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter.
Here,
The perimeter of the square drawn on the grid
The vertices given in the question are (3,3) & (7,7)
The length of the vertices given=[tex]\sqrt{(x_{2} -x_{1})^{2} +(y_{2}- y_{1})^{2} }[/tex]
Thus at vertices (3,3) & (7,7)
=>[tex]\sqrt{(7 -3)^{2} +(7-3)^{2} }[/tex]
=>4[tex]\sqrt{2}[/tex]
Therefore the perimeter of the square = 4a
thus,
=>4*4[tex]\sqrt{2}[/tex]
=>16[tex]\sqrt{2}[/tex] units
Therefore the perimeter of the square on the grid is 16[tex]\sqrt{2}[/tex] units
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For the high school basketball game, it costs $12 for every 3 tickets.
Complete the table below showing the cost and the number of tickets.
Based on the unit rate of the table, the missing values that shows the cost and the number of tickets are:
$32 and 9 tickets.
How to Complete the Table Showing Cost and Number of Tickets?To calculate the missing values in the table shown in the attachment below, we have to find the unit rate, which is the cost of 1 ticket.
Given that 3 tickets will cost $12, therefore:
Unit rate = 12 / 3 = $4 per ticket.
Using this rate, find the missing values as explained below.
For 8 tickets, we will have the following cost:
8 × $4 = $32
For $36, we will have the following tickets:
$36/$4 = 9 tickets
Thus, the missing values that will complete the table will be:
$32 and 9 tickets.
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Eliza bought a hat for $21. The regular price is %30. What percent of the regular price did she pay?
Answer:
27.3
Step-by-step explanation:
21 times 1.3 = 27.3 = original price
She paid 70% of the regular price of $30.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that Eliza bought a hat for $21. The regular price is $30. The percentage will be calculated as,
Percentage = 21 / 30
Percentage = 0.7 x 100
Percentage = 70%
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50 POINTS PLEASE HELP QUICK
Which expression is equivalent to 2 and three tenths raised to the fourth power divided by nine tenths raised to the fifth power, all raised to the fourth power?
A: 2 and three tenths raised to the eighth power divided by nine tenths raised to the ninth power
B: 2 and three tenths raised to the sixteenth power divided by nine tenths raised to the twentieth power
C: 1.4 raised to the forth power
D: 1.4 raised to the ninth power
Answer:
The answer is B
Step-by-step explanation:
I took the test and got it right,(also i have a pic) brainiest pls!!
Solve the system by substitution. { − 4 . 5 x − 2 y = − 12 . 5 3 . 25 x − y = − 0 . 75
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The value of x is 1.
The value of y is 4.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 - 9 = 5 is an equation.
We have,
-4.5x - 2y = -12.5 ____(1)
3.25x - y = -0.75 _____(2)
From (1) we get,
-4.5x + 12.5 = 2y
y = (-4.5x + 12.5) / 2 _____(3)
Now,
3.25x - y = -0.75
Putting (3) in (2) we get,
3.25x - (-4.5x + 12.5) / 2 = -0.75
6.5x + 4.5x - 12.5 = 2 x -0.75
11x - 12.5 = -1.5
11x = -1.5 + 12.5
11x = 11
x = 1
Now,
From (3) we get,
y = (-4.5x + 12.5) / 2
y = (-4.5 x 1 + 12.5) / 2
y = (-4.5 + 12.5) / 2
y = 8/2
y = 4
Thus,
The value of x is 1.
The value of y is 4.
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If you deposit $25,000 now at 6.5% compounded quarterly, how much will you have in 30 years?
Answer:
$172,984.44 (nearest cent)
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]
Given:
P = $25,000r = 6.5% = 0.065n = 4 (quarterly)t = 30 yearsSubstitute the given values into the formula and solve for A:
[tex]\implies A=25000\left(1+\dfrac{0.065}{4}\right)^{4 \cdot 30}[/tex]
[tex]\implies A=25000\left(1.01625\right)^{120}[/tex]
[tex]\implies A=25000\left(6.9193776...\right)[/tex]
[tex]\implies A=172984.4404[/tex]
Therefore, if you deposit $25,000 now at 6.5% compounded quarterly, you will have $172,984.44 (nearest cent) in 30 years.
Quetion The cot c (in dollar) for the fuel and maintenance of a go-cart i given by c=15x1000, where x i the number of ride. It cot $20 per ride. How many ride doe it take to break even?
200 rides does it take to break even.
What are the many sorts of cost?
Fixed and variable costs are the two main categories of expenses incurred by enterprises. While variable costs fluctuate with output, fixed costs do not.
Sometimes, fixed costs are referred to as overhead costs. They must be paid whether a company produces 100 or 1,000 widgets.
The cost function is given by
C(x ) = 15x + 1000
It is also given that it costs $25 per ride.
so,
Revenue function for x number of rides be
R(x) = 20x
For break even:-
The cost must be equal to the Revenue i.,e
C(x) = R(x)
15x + 1000 = 20x
1000 = 20x - 15x
1000 = 5x
x = 1000/5
x = 200
Therefore, 200 rides does it take to break even.
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Lamont works for a company that pays him $20 per hour, but $50 each week is deducted from his pay for insurance. let p(h) represent Lamont's pay in one week after deductions for working h hours. The function
p
(
h
)
=
20
h
−
50
p(h)=20h−50 is used to calculate Lamon's weekly pay after the insurance deduction. What is the independent variable?
The independent variable in the given function is h.
What are Independent and dependent variables?The Independent variables are those variable whose value does not depend on any other variable. And it causes the change in other variables.
The dependent variable is those variables whose value is not independent and change in this variable is dependent on the change of the independent variable.
Given the function p(h)=20h−50, which represents Lamont works for a company that pays him $20 per hour(h), but $50 each week is deducted from his pay for insurance.
Now, in the given function since the amount that Lamont will get depends upon the number of hours for which he is working.
Therefore, the h is the independent variable and p is the dependent variable.
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What is y=-2x+5 in standard form
Answer: 2x+y=5
Step-by-step explanation:
The standard form of a linear equation is
ax+by=c
Move all terms containing variables to the left side of the equation.
2x+y=5
Answer:
2x + y = 5
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Standard form of a linear equation}\\\\$Ax+By=C$\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are constants. \\ \phantom{ww}$\bullet$ $A$ must be positive.\\\end{minipage}}[/tex]
Given equation:
[tex]y=-2x+5[/tex]
To write the given equation in standard form, collect the terms with variables on one side of the equation, ensuring the term in x is positive.
Add 2x to both sides:
[tex]\implies y+2x=-2x+5+2x[/tex]
[tex]\implies y+2x=5[/tex]
[tex]\implies 2x+y=5[/tex]
Joseph and Raquel are building a scale model of the Alamo Mission for their Texas history project using a scale in which 2 inches represents 30 feet. The enclosed area of the Alamo Mission was 480 feet long and 160 wide.
What should the length of the enclosed area of the scale model be in inches?
Th length of the enclosed area of the scale model in inches is 32 inches.
How to find the length of the enclosed area of the scale model in inches?Joseph and Raquel are building a scale model of the Alamo Mission for their Texas history project using a scale in which 2 inches represents 30 feet.
The enclosed area of the Alamo Mission was 480 feet long and 160 feet wide.
The length of the enclosed area of the scale model in inches can be calculated as follows:
30 feet = 2 inches
480 feet = ?
cross multiply
length of the enclosed area = 480 × 2 / 30
length of the enclosed area = 960 / 30
length of the enclosed area = 32 inches
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Mr. Miller weigh 180pound. If hi weight decreae by 10% how much i hi new weight?
In linear equation, 162 is his new weight .
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Mr. Miller weigh = 180pound
10% decrease = 180 * 10/100
= 18
new weight = 180 - 18
= 162
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x-½y=0 ½x- 0 ½z=-1 3x-y -z =-2
You currently have $40 saved up. You get $5 every
time you shovel the driveway. Your friend has no
money saved up and gets $10 every time she
shovels her driveway (hers is twice as big as
yours!) After how many driveways will you have
the same amount of money as your friend?
Help me with ixl please
Answer:
∠AFB
Step-by-step explanation:
Vertical angles are opposite to one another and share the same vertex or endpoint. ∠DFE is ∠AFE both share the point F, and they are opposite to each other, so they are also vertical to each other.
Find the coordinates of the circumcenter of the triangle with the given vertices.
A(2, 2). B(2, 4), C(8, 4)
The circumcenter is
Answer:D
beacuse it is correct just trust me i have done this class and its correct
Solve for x
48° 73° X°
Answer:
[tex]x=59[/tex]
Step-by-step explanation:
Angles in a triangle add to [tex]180^{\circ}[/tex].
[tex]\implies x=180-48-73=59[/tex]
What is the location of point G, which partitions the directed line segment from D to F into a 5:4 ratio? –1 0 2 3
The location of G is (3, 0).
Given question in that we have a number line.
A number line goes from negative 5 to positive 10.
Point D is at negative 2 and point F is at positive 7.
A line is drawn from point D to point F.
So we can write coordinate of point D as (-2,0) and point F as (7,0).
line segment from D to F divides as point G as in ratio of 5:4
Consider two points P(x1, y1) and Q(x2, y2). We have to find the coordinates of the point R which divides PQ in the ratio m : n
x = [tex]m*x2+n*x1/(m + n)[/tex]
[tex]y = m*y2+n*y1/(m + n)[/tex]
so here in our question m =5 n=4
x1=-2 x2=7 y1=0 y2=0
x = 5*7+4*(-2)/9
x = 3
y = 5*0+4*0/9 = 0
So the location of G is (3, 0)
Given Question is incomplete complete question here.
What is the location of point G, which partitions the directed line segment from D to F into a 5:4 ratio? A number line goes from negative 5 to positive 10. Point D is at negative 2 and point F is at positive 7. A line is drawn from point D to point F.
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PLEASE HELP ME I GIVE YOU POINTS
Answer:1.44
Step-by-step explanation:
If A+K=4 and AK=3 then find the vale of A³+K³
Answer:
Below
Step-by-step explanation:
k = 4-a
a (4-a) = 3
-a^2 +4a -3 = 0 ====> Quadratic Formula ===> a = 1 and k = 3
1^3 + 3^3 = 28
Sam purchased a 30$ bus pass. Each time they ride the bus, $2.25 is deducted. Write an equation to show the amount of money left on the bus pass after x rides.
Answer:
-2.25x = 30
Step-by-step explanation:
I hope this helps!