Answer:
Step-by-step explanation:
Let's first find the number of 12-year-olds and 13-year-olds in the band:
Let x be the number of 12-year-olds.
Then the number of 13-year-olds is 1.25x (125% of x).
The total number of students in the band is 100, so we know that x + 1.25x = 0.9(100).
Solving for x, we get x = 40, so there are 40 12-year-olds and 50 (1.25x) 13-year-olds.
The number of 14-year-olds is the remainder after we count the 12 and 13-year-olds:
The total number of students in the band is 100, and we know that 90% of them are 12 or 13 years old, so 10% are 14 years old.
10% of 100 is 10, so there are 10 14-year-olds.
Now we can find the portion of the band for each age group:
12-year olds: fraction = 40/100 = 2/5, percent = 40%
13-year olds: fraction = 50/100 = 1/2, percent = 50%
14-year olds: fraction = 10/100 = 1/10, percent = 10%
There are 50 volunteers to start a community service project. The project organizer expects this number to increase by 6% every hour for the next
5 hours. If the organizer is correct, which value is closest to the number of volunteers the project will have at the end of five hours?
63
65
67
71
In 6th grade you likely solved which one is a better buy problems?
Consider: $68/10 tickets or $15/2 tickets
Which one is a better buy? How do you know?
$68/10 is better to buy as price of one ticket will be $6.8 which is less than that of $7.5 for other ticket.
Explain about the unit value?The appraisal of a single item or part within one group is known as unit value.
The unit value is typically the result of dividing the price or worth of a set of things by the total number of items.The unit price is the cost of a single object or measuring unit, which can be a pound, a kilogramme, or a pint, and it's utilized to compare the prices of similar products offered in various weights and quantities. Selling more than one unit of the same product at a discount from its unit price is known as multiple pricing.So,
$68/10 tickets = 68/10
$68/10 tickets = $6.8 for each ticket.
Now,
$15/2 tickets = 15/2
$15/2 tickets = $7.5 for each ticket.
Thus, $68/10 is better to buy as price of one ticket will be $6.8 which is less than that of $7.5 for other ticket.
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The question is in the photo
The value of y, given that Triangle FEG is similar to Triangle IHJ is 10.
How to find the value of y ?Seeing as Triangle FEG is similar to Triangle IHJ, we can assume that angle EGF is the same as angle HJ1.
This means that 5 y + 8 is equal to 58 degrees.
The value of y is therefore :
5 y + 8 = 58
5 y = 50 - 8
y = ( 50 - 8 ) / 5
y = 50 / 5
y = 10
In conclusion, given the two similar triangles and the angles EGF and HJI, the value of y can be found to be 10.
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What is the volume of the triangular prism?
PLS HELP!!
Answer:
20cm³
Step-by-step explanation:
Volume = Base x Height
1/2 x 5 x 2 x 4
=20cm³
WILL MAKRK AS BRAINLIEST!!!!!
A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the area of the largest possible Norman window with a perimeter of 34 feet?
The dimensions of the window that maximize the area of the window is x = 17/(π - 1)(2) and y = 17 - (17/(π - 1)(2)) (1 + π ).
What is area?An area is just a surface that is empty. The length and breadth of a form are used to compute its area. The units used to measure length are unidimensional and include feet (ft), yards (yd), inches (in), etc. Nevertheless, a shape's area can only be measured in two dimensions. As a result, it is expressed in square units such as square inches (in2), square feet (ft 2), square yards (yd2), etc. Most forms and things have edges and corners. When determining an object's area, the length and breadth of these edges are taken into account.
Let us suppose the width of the rectangle = x.
The length of the rectangle = y
Thus,
Perimeter = 2 (x + y) + πx
34 = 2x + 2y + πx
2y = 34 - 2x + πx
The area of the window is:
A = (1/2)πx²+ xy
Substitute y = 34 - 2x + πx / 2
To maximize the area we differentiate the area and equate it to 0:
A = (1/2)πx²+ x(34 - 2x + πx / 2)
A = (1/2)πx²+ 17x - x² + π/2x²
dA/dx = πx + 17 - 2x + πx
2πx + 17 - 2x = 0
2x(π - 1) = - 17
x = 17/(π - 1)(2)
Substitute the value of x in equation:
2y = 34 - 2x + πx
2y = 34 - 2(17/(π - 1)(2)) + π( 17/(π - 1)(2))
y = 17 - (17/(π - 1)(2)) (1 + π )
Hence, the dimensions of the window that maximize the area of the window is x = 17/(π - 1)(2) and y = 17 - (17/(π - 1)(2)) (1 + π ).
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first increase and then rework each by decreasing
a. 400 by 20%
b. 650 by 30%
c.820 by 45%
d. 150 by 2,5%
e. 300 by 5%
f. 420 by 2,5%
Answer:
a. 480 Then 384
b. 845 Then 591.5
c. 1,189 Then 653.95
d. 153.75 Then 149.90625
e. 315 Then 299.25
f. 430.5 Then 419.7375
Which equation has the same solution set as (x - 3)² = 0 ?
-2x²-18
x²-9=0
x² + 6x = -9
12x -18=2x²
Answer:
x^2 - 9 = 0
Step-by-step explanation:
its right one.......
100 POINTS!!!! ILL GIVE BRAINLEIST. What is true when two proper fractions are multiplied together?
The product will be larger than both factors.
The product will be larger than the smaller factor but smaller than the larger factor.
The product will be smaller than both factors.
The product will be an improper fraction.
Answer:
When two proper fractions are multiplied together, the product will be smaller than both factors.
Step-by-step explanation:
To understand why this is true, we can consider the concept of fractions as parts of a whole. When we multiply two proper fractions, we are essentially taking a part of a part, which results in a smaller portion overall.For example, if we multiply 1/2 by 2/3, we are taking half of something and then taking two-thirds of that half. The result is 1/3, which is smaller than both 1/2 and 2/3.Therefore, the correct answer is: The product will be smaller than both factors.
Answer:The product will be smaller than both factors.
When two proper fractions are multiplied together The product will be smaller than both factors.Take a look at the equation below.
¾ * ⅔= 3 times 2 is 6 and 4 times 3 is 12. So the equation is 6/12 .
6/12 is simplified to 1/2. 1/2 is less than both 2/3 and 3/4. Which means the product is smaller. Hence, the correct answer is the product will be smaller than both factors.
I hope this helped & Good Luck <3!!!!
Given a right triangle, ABC, where C = 90° and AB = 8 in. and BC = 3 in. Determine the exact value of cot (A).
The value of cot A is √55/3
What is trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.
cot A = 1/tanA
AC = √ 8²-3²
AC = √64-9
AC = √ 55
tanA = 3/√55
cot A = 1/tanA
cot(A )= 1/(3/√55)
cot( A) = √55/3
therefore the value of cot(A) = √55/3
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The Clarke's son suggests that they rent a car that costs $250 for the week plus $0.22c/km. Their daughter does not want to drive far, so she suggests a car that is only $96 for the week but $0.50/km.
a) Write an equation to represent the cost of the car suggested by the son
b) Write an equation to represent the cost of the car suggest by the daughter
c) When will the two cars cost the same? Used the method of elimination to solve.
d) If the Clarke's plan to drive 500km, which option is less expensive?
Answer: a) The equation to represent the cost of the car suggested by the son is:
C1 = 250 + 0.22k
where C1 represents the total cost of renting the car, and k represents the number of kilometers driven.
b) The equation to represent the cost of the car suggested by the daughter is:
C2 = 96 + 0.5k
where C2 represents the total cost of renting the car, and k represents the number of kilometers driven.
c) To find when the two cars cost the same, we need to solve the equation:
C1 = C2
Substituting the expressions for C1 and C2 from parts a and b, we get:
250 + 0.22k = 96 + 0.5k
Simplifying this equation, we get:
0.28k = 154
Dividing both sides by 0.28, we get:
k = 550
Therefore, the two cars cost the same when the number of kilometers driven is 550.
d) If the Clarke's plan to drive 500km, we can calculate the total cost for each car by substituting k=500 into the equations from parts a and b:
C1 = 250 + 0.22(500) = 360
C2 = 96 + 0.5(500) = 346
Therefore, the car suggested by the daughter is less expensive for a 500km trip, as it would cost $346 compared to $360 for the car suggested by the son.
Step-by-step explanation:
- Two dry cleaning companies offer a home pick-up and delivery service. The monthly cost depends on the number of garments laundered, and is shown in the following table.
Number of Garments
5
10
15
Company 1
$55.25
$75.50
$95.75
Company 2
$31.25
$57.50
$83.75
The ordered pair representing the point where both companies would charge the same amount is (25, 136.25).
When would both companies charge the same amount?
From the given table, we can form the following equation for monthly cost of each company.
Company 1, the function for the monthly cost is;
(5, $55.25 ) and (10, $75.5). Let the monthly cost = y₁
(y₁ - 55.25 )/(x - 5) = ( 75.5 - 55.25 )/ (10 - 5)
y₁ = 4.05x + 35
Company 2, the function for the monthly cost is;
(5, $31.25 ) and (10, $57.5). Let the monthly cost = y₂
(y₂- 31.25 )/(x - 5) = ( 57.5 - 31.25 )/ (10 - 5)
y₂ = 5.25x + 5
To find the point where both companies charge the same amount, we need to set their costs equal to each other and solve for the number of garments, x:
y₁ = y₂
4.05x + 35 = 5.25x + 5
Subtracting 4.05x and 5 from both sides:
30 = 1.2x
Dividing both sides by 1.2:
x = 25
So both companies would charge the same amount when 25 garments are laundered. T
To find the cost, we can plug x = 25 into either equation:
y₁ = 4.05(25) + 35 = 136.25
y₂ = 5.25(25) + 5 = 136.25
Ordered pair = (25, 136.25)
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The complete question is below:
Two dry cleaning companies offer a home pick-up and delivery service. The monthly cost depends on the number of garments laundered, and is shown in the following table.
Number of Garments Company 1 Company 2
5 $55.25 $31.25
10 $75.50 $57.50
15 $95.75 $83.75
Determine when both companies would charge the same amount and what that cost would be. Write your answer as an ordered with x representing the number of garments and y representing the cost.
The shape below is a rhombus.
a) Which side is parallel to PQ?
b) Which angle is the same size as angle
QRS?
P
S
R
RS is Parallel to PQ and ∠ P has the same size as ∠ QRS. We find the answer by knowing the definition of Rhombus.
What is a rhombus?Rhombus is a special case of a parallelogram having four equal sides and opposite equal acute and obtuse angles . The term "equilateral quadrilateral" refers to a quadrilateral whose sides all have equal lengths i.e. Rhombus.
In mathematics, a parallelogram is a simple (non-self-intersecting) quadrilateral with two sets of parallel sides.
a. RS is Parallel to PQ
b. ∠ P has the same size as ∠ QRS
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Select the graph that represents the solution of the compound inequality –6 ≤ 4x + 6 < 14
By answering the above question, we may state that The range of -3 x 2 inequality is the answer to the compound inequality.
What is inequality?A connection between two expressions or values that is not equal in mathematics is referred to as an inequality. Hence, inequity results from imbalance. In mathematics, an inequality establishes the connection between two non-equal numbers. Egality and inequality are not the same. Use the not equal symbol most frequently when two values are not equal (). Values of any size can be contrasted using a variety of inequalities. By changing the two sides until just the variables are left, many straightforward inequalities may be solved. Nonetheless, a variety of factors support inequality: Both sides' negative values are split or added. Exchange the left and the right.
We must first remove 6 from each of the three elements of the compound inequality -6 4x + 6 14 in order to arrive at the following result:
-6 - 6 ≤ 4x < 14 - 6
If we simplify, we get:
-12 ≤ 4x < 8
Then, we divide each of the three inequality components by 4, keeping in mind that we don't need to reverse the inequality's signs because 4 is positive, to arrive at:
-3 ≤ x < 2
The range of -3 x 2 is the answer to the compound inequality.
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The back of a garbage truck is 23 feet long, 8 feet wide, and 12 feet tall. How many loads of trash from the garbage truck will it take to fill a 40 foot by 9 foot by 8 foot storage container?
it will take approximately 1.30 loads of trash from the garbage truck to fill the 40-foot by 9-foot by an 8-foot storage container. However, since you can't have a partial load, you would need to round up to 2 loads to completely fill the container.
what is an algebraic expression?
An algebraic expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that can be simplified and evaluated.
To determine the number of loads of trash from the garbage truck that will fill a 40-foot by 9-foot by 8-foot storage container, we need to compare the volume of the container to the volume of the garbage truck's back.
The volume of the garbage truck's back is:
V_garbage_truck = length x width x height
V_garbage_truck = 23 ft x 8 ft x 12 ft
V_garbage_truck = 2,208 cubic feet
The volume of the storage container is:
V_container = length x width x height
V_container = 40 ft x 9 ft x 8 ft
V_container = 2,880 cubic feet
To find out how many loads of trash from the garbage truck will fill the storage container, we need to divide the volume of the container by the volume of the garbage truck's back:
Number of loads = V_container / V_garbage_truck
Number of loads = 2,880 cubic feet / 2,208 cubic feet
Number of loads ≈ 1.30 loads
Therefore, it will take approximately 1.30 loads of trash from the garbage truck to fill the 40-foot by 9-foot by an 8-foot storage container. However, since you can't have a partial load, you would need to round up to 2 loads to completely fill the container.
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Solve for x. Leave as an improper fraction. 5 = 3x + 9
Answer:
x = -4/3
Step-by-step explanation:
hope this helps^^
Write each amount as rate
500 words in one minute
Answer:
500 words per minute.
Step-by-step explanation:
Find the area of the figure.
Answer:
16yd
Step-by-step explanation:
I am from Michigan thank me this is really easy you nerd
This is funny helping you big people as a kid.
Brainliest for correct answer
Which graph best represents the function f(x)=4x−4f(x)=4x−4?
The best represent graph of the function is option a.
What is a function?
It is an expression which contains one independent variable and another is dependent variable.
The given function is
f(x)= [tex]4^{x[/tex] - 4
As it is an exponential function so it must have a horizontal asymptote. Here the horizontal asymptote is f(x)= -4
For x intercept we need to take f(x)=0 and for y intercept substitute 0 for x and solve for y. [Here y can be treated as f(x).]
Here x intercept(s)= None
y intercept(s) = (0,-3)[ putting x=0 in f(x) so 1-4= -3]
Hence the graph is given below.
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2. Is AP'Q'R' a 180° rotation about the origin of APQR?
Explain.
4
t
2
20
2
d
P
R
2 4
4.
R
à x*
8
It should be noted that AP'Q'R' a 180° rotation about the origin of APQR.
How to explain the rotationIt should be noted that to perform a 180° rotation about the origin, one has to draw the original figure and label its coordinates and draw the origin and label it O.
One can also use the following formula to find the coordinates of the image of a point (x,y) after a 180° rotation about the origin:
(x', y') = (-x, -y)
Here, P'Q'R' represents the coordinates of the image of the point PQR. We simply take the negative of the original x and y coordinates to find the new coordinates after the rotation.
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NEED THIS DUE BY TODAY!!
1) The volume of the first rectangular prism is 175 ft³
2) The volume of the second rectangular prism is 60ft³
3) The volume of the third rectangular prism 140ft³
4) The volume of the Fourth rectangular prism 216ft³
What is the rationale for the above response?Note that in order to find the volume of area of a complex figure, you must deconstruct it into manageable proportions.
Shape 1 above, we deconstructed the rectangular prism into two 3 dimensional shapes with the following metrics:
a)
Length = 7ft
Height = 2ft
widht = 2ft
Volume = Volume = 7ft x 2ft x 2ft
Volume = 28 ft³
b)
Length = 7ft
Height = 3ft
width = 7ft
Volume = 147 ft³
Total Volume = 28 ft³ + 147 ft³
Volume for Shape 1 = 175 ft³
Shape 2 above, we deconstructed the rectangular prism into two 3-dimensional shapes with the following metrics:
a) Length = 3ft
Height = 2ft
width = 1ft
Volume = 6 ft³
b) Length = 6ft
Height = 3ft
width = 3ft
Volume = 54 ft³
Thus, total volume for shape 2 is:
Volume = 6 + 54
Volume = 40 ft³
Shape 3, above, we deconstructed the rectangular prism into two 3-dimensional shapes with the following metrics:
a) Length = 7ft
Height = 1ft
width = 2ft
Volume = 14ft³
b)
Length = 7ft
Height = 3ft
width = 6ft
Volume = 126ft³
Thus, the total volume fior shape 3, =
Volume = 14ft³ + 126ft³
Volume = 140ft³
Shape 4, above, we deconstructed the rectangular prism into two 3-dimensional shapes with the following metrics:
a) Length = 4ft
Height = 3ft
width = 2ft
Volume = 24 ft³
b) Length = 4ft
Height = 12ft
width = 4ft
Volume = 192 ft³
Thus, the total volume for Shape 4:
Volume = 24 ft³+ 192 ft³
Volume = 216ft³
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the price of a ticket on the local commuter train can be determined from the expression 1.35 + 0.40(s), where s is the number of stops for which the passenger will be on the train
The price οf the ticket when the number οf stοps is 13, fοund using the given expressiοn, is $6.55.
What is an expressiοn?Mathematical expressiοns cοnsist οf at least twο numbers οr variables, at least οne maths οperatiοn, and a statement. It's pοssible tο multiply, divide, add, οr subtract with this mathematical οperatiοn. A finite cοmbinatiοn οf symbοls that are well-fοrmed in accοrdance with cοntext-dependent principles is referred tο as an expressiοn οr mathematical expressiοn. There are twο sοrts οf expressiοns in mathematics: numerical expressiοns, which οnly cοntain numbers, and algebraic expressiοns, which alsο include variables. Expressiοns can be categοrised as arithmetic/numerical expressiοns, fractiοnal expressiοns, οr algebraic expressiοns depending οn the terms they cοntain.
Given the expressiοn as:
1.35 + 0.40(s)
This is used tο calculate the price οf a ticket οn the lοcal cοmmuter train.
s = number οf stοps
Nοw the cοmplete questiοn is tο calculate the price οf the ticket fοr 13 stοps.
Sο s = 13
Substitute in the expressiοn,
1.35 + 0.40(s) = 1.35 + 0.40 * 13 = 1.35 + 5.2 = $6.55
Therefοre the price οf the ticket when the number οf stοps is 13, fοund using the given expressiοn, is $6.55.
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Find the slope of a line parallel to the line whose equation is
5
�
−
3
�
=
18
5x−3y=18. Fully simplify your answer.
The slope of a line parallel to the line whose equation is 5x - 3y = 18 is equal to 5/3.
What is the slope-intercept form?In Mathematics, the slope-intercept form of an equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m is the gradient, slope, or rate of change.x and y represent the points.c represents the y-intercept or initial value.Making y the subject of formula, we have the following:
5x - 3y = 18
3y = 5x - 18
y = 5x/3 - 6
In Geometry and Mathematics, two (2) lines are said to be parallel under the following conditions:
m₁ = m₂ ⇒ 5/3 = 5/3
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I need help on this question please anyone ?!!!!??!!!
PLEASE GIVE BRAINLIEST <3
Answer:
I'm pretty sure it's bumper cars ( B ).
Hope this helped! <3
Find the values of x and y.
The value of x and y in the triangle are 0 and 4 respectively.
How to find the side of a triangle?The mid segment of a triangle is a line connecting the midpoints between two sides of a triangle. The mid segment theorem states that the midsegment connecting the midpoints of two sides of a triangle is parallel to the third side of the triangle, and the length of this midsegment is half the length of the third side .
Therefore,
x + 2 = 3 / 2 x + 2
x - 3 / 2 x = 2 - 2
-0.5x = 0
x = 0
Let's find y
2y - 1 = 3y - 5
2y - 3y = -5 + 1
-y = -4
y = 4
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i need help asap it is homework
Answer:
See below.
Step-by-step explanation:
Hello!
The topic we should review for this problem is Order of Operations.
What is Order of Operations?
Order of Operations is a rule that identifies which part of an equation should be simplified first.
You might've heard of PEMDAS, where;
P for Parentheses, always first unless there's an exponent inside.
E for Exponent, simplified after the Parentheses.
M or D - Multiplication or Division after the Exponent(s).
A or S - Addition or Subtraction after Multiplication or Division.
[tex](5+3^2)+18[/tex]
First we know that there's an Exponent inside the Parentheses, so we must evaluate that number first.
[tex](5+9)+18[/tex]
Next, evaluate what's in the Parentheses.
[tex]14+18\\32[/tex]
Our correct answer is 32.
We are asked what mistake did Raquel make, and what's the correct simplified version of the expression.
1a.) Raquel's mistake is combining unlike terms. It's impossible to combine together a natural number (5) and an exponential number. (3²)
1b.) The correct simplified version of the expression is represented here;
[tex](5+9)+18\\(First \ Step)[/tex]
What's the value of X and Y?
(Need answers SUPER fast, please and ty!)
Answer:
x = 9/4 y = 15/4
Step-by-step explanation:
Write the set using the roster method.
Set D is the set of positive two-digit even numbers greater than 74
that do not contain the digit 8
.
The set using Roster method is, D = {76, 90, 92, 94, 96}
What is Roster Method?The roster technique is defined as a method for displaying the elements of a set by listing the elements within brackets.
A roster method example is to write the set of numbers from 1 to 10 as
{1, 2, 3, 4, 5, 6, 7, 8, 9, and 10}.
Given:
Set D is the set of positive two-digit even numbers greater than 74
that do not contain the digit 8
First, Even numbers greater than 74 are
76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98.
Now, Even Number doe not contain 8 are 76, 90, 92, 94, 96.
Using Roster method the set is
D= {76, 90, 92, 94, 96}
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5. 100 people have food for 20 days at the rate 2kg per person per day. If 20 people left, how long will the food last if they eat (a) 2kg per person daily? (b) 1.8 kg per person daily?
Answer:
25
Step-by-step explanation:
let the no of days food avl for eat be X .
according to question...
100/80=X/20
=X × 80 = 100×20
=80x =2000
= x =2000/80
x=25 days
D=25 m
39⁰
Can someone work this out so I can check my answers thanks !
Answer:[tex]m[/tex] = [tex]d[/tex]/[tex]25[/tex]
Step-by-step explanation:I don't know if this is correct but i think it is:
Solve D=25m
Evaluate powers D = 25m
Subtract D from both sides D= 25m[tex]1[/tex] - D
Add D to both sides D=25m1
Evaluate powers D=25m
Divide both sides by 25 D/25 =m
Solution m = D/25