The expression representing the total number of people involved in the competition is 2n + 5.
What are Algebraic Expressions?Algebraic expressions are defined as the statements in mathematics which consist of constants, coefficients of the variables and variables connecting with basic operations like addition, multiplication, subtraction, etc.
Algebraic equations are something with an algebraic expression equal to something. But in algebraic expressions, there will be no equal to sign.
There are basically three classes of algebraic expressions, namely, monomial, binomial and polynomial expressions.
Number of couple dancing in a competition = n
Number of people involving in a couple dance is 2.
Total number of people dancing as couple = 2n
Number of organizers in the competition = 5
Total number of people involved = 2n + 5
Hence 2n + 5 number of people are involved in the competition program.
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You are opening a savings account with $500 that you have saved. The bank offers 3.2% interest, compounded yearly. How much money will you have in you account after 7 years?
Answer:
You will have $623.3441462 in your account after 7 years
Step-by-step explanation:
The formula of the compounded interest is A = P [tex](1+\frac{r}{n})^{nt}[/tex] , where
A is the new valueP is the initial valuer is the rate in decimaln is the number of periodst is the time in years∵ You are opening a savings account with $500
∴ P = 500
∵ The bank offers 3.2% interest, compounded yearly
∴ r = 3.2% ⇒ divide it by 100 to change it to decimal
∴ r = 3.2 ÷ 100 = 0.032
∵ The interest is compounded yearly
∴ n = 1
∵ The time is 7 years
∴ t = 7
→ Substitute these values in the rule above to find A
∵ A = 500 [tex](1+\frac{0.032}{1})^{1(7)}[/tex]
∴ A = 500 [tex](1.032)^{7}[/tex]
∴ A = 623.3441462
∴ You will have $623.3441462 in your account after 7 years
easy question in photo
Answer:
14
Step-by-step explanation:
always subtract the highest number from the lowest and I believe that is your range
Answer:
14
Step-by-step explanation:
Solve the system: (MAFS.912-A-REI.3.6)
4+7=41
4
x
+
7
y
=
41
4+7=41
4
x
+
7
y
=
41
−7=−16
Step-by-step explanation:
[tex]4x + 7y = 41 \\ 4 \times ( - 7) + 7 \times ( - 16) = 41[/tex]
I really need help. And its setted up-
Answer:
4: 300
5: 95
have a good day :]
plss help me find this hcf
3a-6,a²-4
Step-by-step explanation:
1st expression = 3a - 6 = 3 ( a - 2 )
2nd expression = a² - 4 = a² - 2² = ( a + 2) (a - 2)
The HCF is (a -2).
Hope it helps :)❤
choose the definition for the function y={x+1 x≤2 x+2 x>2 y={x+1 x>2 x+2 x≤2 y={x+1 x
Answer:
D
Step-by-step explanation:
A 24-f0ot ladder rests against a house near a second story window 20 feet from the ground. Assume that the ladder
and the house both stt on level ground.
To the nearest whole nurmber, find the following values:
A The measure of the angle formed by the base of the ladder and level ground is
B. The measure of the angle formed by the top of the ladder and the second story window is
C. The distance, on level ground, between the base of the ladder and the house is
feet
degrees.
feet.
Answer:
c
Step-by-step explanation:
Paul's basketball coach decides that he will play only the first three quarters of every game this season. If he starts
the first 20 games, what expression can you write to model how much playing time he actually gets?
o 3.20
O = 20
o * + 20
03 - 20
Answer:
im thinking the answer is 3/4 x 20
Answer:
3.20
Step-by-step explanation:
i used math
Write the equation in slope-intercept form.
(2,-3) and (1,3)
Determine the constant of proportionality in each of the representations below.
Answer:
Pretty sure is 15
Step-by-step explanation:
90 divided by 6 is 15.
Answer:
The constant of proportionality, k is 15
Step-by-step explanation:
The constant of proportionality is the ratio between two directly proportional quantities.
Proportional quantities can be described by the equation y = kx, where k is a constant ratio.
Here, "x" is the number of tickets and "y" is the number of dollars.
k = 30/2 = 15/1 or 15
k = 15
k = 60/ 4 = 30/2 = 15/1 or 15
k = 15
k = 90/6 = 30/2 = 15/1 0r 15
k = 15
When we take the ratio of x and y for all the given values, we get an equal value for all the ratios.
Therefore, the constant of proportionality, k is 15
There are 25 students in Mrs. Murphy's math class. Of these students, 10 have brown hair, 8 have black hair, 5 have blonde hair, and 2 have red hair. What percentage of students in Mrs. Murphy's class have blonde hair?
The percentage of students in Mrs. Murphy's class who have blonde hair will be 20%.
What is the percentage?The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.
There are 25 students in Mrs. Murphy's math class. Of these students, 10 have brown hair, 8 have black hair, 5 have blonde hair, and 2 have red hair.
Then the percentage of students in Mrs. Murphy's class who have blonde hair will be
Total students = 25
Then we have
[tex]\rm P = \dfrac{5}{25} \times 100\\\\P = 0.20 \times 100\\\\P = 20 \%[/tex]
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Joe bought some CD's and DVD's at the store.
• He bought a total of 12 items.
• The CD's were $14.
• The DVD's were $22.
• He spent $200.
How many of each did he buy?
Answer: x=8 and y=4
Step-by-step explanation:
x+y=12 x=12-y x=12-4
14x+22y=200 x=8
14(12-y)+22y=200
168-14y+22y=200
-168 -168
-14y+22y=32
8y=32
8y/8=32/8
y=4
Consider the function represented by 9x + 3y = 12 with x as the independent variable. How can this function be
written using function notation?
O FU=-v+
Of(x) = - 3x + 4
o f(x) = -x +
Of = -3y + 4
Answer:
9x + 3y = 12
3y = -9x + 12
y = -3x + 4
f(x) = -3x + 4
Step-by-step explanation:
I hope it's help
If $12000 is invested in an account in which the interest earned is continuously compounded at a rate of 2.5%
Complete Question
If $12000 is invested in an account in which the interest earned is continuously compounded at a rate of 2.5% for 3 years
Answer:
$ 12,934.61
Step-by-step explanation:
The formula for Compound Interest Compounded continuously is given as:
A = Pe^rt
A = Amount after t years
r = Interest rate = 2.5%
t = Time after t years = 3
P = Principal = Initial amount invested = $12,000
First, convert R percent to r a decimal
r = R/100
r = 2.5%/100
r = 0.025 per year,
Then, solve our equation for A
A = Pe^rt
A = 12,000 × e^(0.025 × 3)
A = $ 12,934.61
The total amount from compound interest on an original principal of $12,000.00 at a rate of 2.5% per year compounded continuously over 3 years is $ 12,934.61.
On a standardized test, Rasi answered the fast: 22 questions in 5 minutes. There are 7]
questions on the test. If he continues to answer questions at the same rate how long will
it take him to complete the test?
Answer:
they are directly proportional
so
5/22*7=1.59
he would finish in 1.59 min
Help would be great thank you!
Answer:
I think 3x doesn't belong because it is the only positive number.
I think -5x doesn't belong because it is the only one without a 3.
I think -3 doesn't belong because it is the only one without an x.
I think -3x² doesn't belong because it is the only one with an exponent.
Step-by-step explanation:
Just use one of the ones above!
(hope this helps!)
1234567791234556677889
Step-by-step explanation:
The rate of pictures per minute.
8 pictures per minute
8 pictures/ minute
Using trigonometry Solve the triangle please help me
Answer:
The angle m ∠ W = 33°
The length of XZ = 9.8 units
The length of WX = 15.1 units
Step-by-step explanation:
Given
The right-angled triangle ΔWXZ
m ∠ X = 90°m ∠ Z = 57°Hypotenuse WZ = 18We know that the sum of the measure of angles in any triangle is 180°.
Therefore,
m ∠ W + m ∠ X + m ∠ Z = 180°
substiute m ∠ X = 90° and m ∠ Z = 57° in the formula
m ∠ W + 90° + 57° = 180°
m ∠ W + 147 = 180°
m ∠ W = 180° - 147
m ∠ W = 33°
Therefore, the angle m ∠ W = 33°
NOW,
Determining the lengths of WX and XZ
Length XZ
Using the trigonometric ratio
The adjacent to 57° is XZ.
so
cos 57° = adjacent / hypotenuse
substituting adjacent = XZ, and hypotenuse = 18
cos 57° = XZ / 18
XZ = 18 × cos 57°
XZ = 9.80 units
Therefore, the length of XZ = 9.8 units
Length WX
As
m ∠ W = 33°
The adjacent to m ∠ W = 33° is WX.
so
cos 33° = adjacent / hypotenuse
substituting adjacent = WX, and hypotenuse = 18
cos 33° = WX/ 18
WX = 18 × cos 33°
WX = 15.1 units
Therefore, the length of WX = 15.1 units
Summary:
The angle m ∠ W = 33°
The length of XZ = 9.8 units
The length of WX = 15.1 units
Please helppp 21 points pleaseeeeeeee. If you don’t know the answer don’t answer please.
Answer:
f(x)=50x+20
0<x x<2
Step-by-step explanation:
hope it helps!
The diagram shows a square based cuboid. Work out the volume of the cuboid. State the units of your answer.
Answer:
160cm³
Step-by-step explanation:
square based means equal sides
therefore 4cm×4cm=16cm²
16cm²×10cm=160cm³
What is the degree of 9x^4 + 3x
Answer:
4
Step-by-step explanation:
ASAP! Please do 1-5 and show work if possible!
Answer :
(1) The radius of a circle is 1.5 m.
(2) The diameter of a circle is 28 ft.
(3) The radius of a circle is 10 in.
(4) The circumference of circle is 47.14 m.
(5) The circumference of circle is 44 yd.
Step-by-step explanation :
Part 1:
Given: d = 3 m
Now we have to determine the radius of circle.
As we know that:
Radius of a circle = [tex]\frac{Diameter}{2}[/tex]
So,
Radius of a circle = [tex]\frac{3m}{2}=1.5m[/tex]
The radius of a circle is 1.5 m.
Part 2:
Given: r = 14 ft
Now we have to determine the diameter of circle.
As we know that:
Radius of a circle = [tex]\frac{Diameter}{2}[/tex]
So,
Diameter of a circle = [tex]Radius\times 2[/tex]
Diameter of a circle = [tex]14ft\times 2=28ft[/tex]
The diameter of a circle is 28 ft.
Part 3:
Given: d = 20 in
Now we have to determine the radius of circle.
As we know that:
Radius of a circle = [tex]\frac{Diameter}{2}[/tex]
So,
Radius of a circle = [tex]\frac{20in}{2}=10in[/tex]
The radius of a circle is 10 in.
Part 4:
Given: d = 15 m
Now we have to determine the circumference of circle.
Formula used:
[tex]C=\pi d[/tex]
where,
C = circumference
d = diameter
So,
[tex]C=\frac{22}{7}\times 15m[/tex]
[tex]C=47.14m[/tex]
The circumference of circle is 47.14 m.
Part 5:
Given: r = 7 yd
Now we have to determine the circumference of circle.
Formula used:
[tex]C=\pi d[/tex]
or we can write,
[tex]C=\pi (2\times r)[/tex]
where,
C = circumference
d = diameter
r = radius
So,
[tex]C=\frac{22}{7}\times (2\times 7yd)[/tex]
[tex]C=44yd[/tex]
The circumference of circle is 44 yd.
Determine the value of x in the diagram.
Answer:
65
it's 65 because it is.. cool
Travis scored 18 point in the first basketball game of the season. he scored 3 fewer points in the second game than in the first game. find the total number of points Travis scored in the first and second games.
Answer:
isn't it 33?
Step-by-step explanation:
because at first they said he scored 18 and the second time he scored 3 fewer points than the first one so its 18+(18-3)=33
pls help
Quadrilateral ABCD is an isosceles trapezoid. What is the m∠B?
Answer:
<B=105°
Step-by-step explanation:
as it's an isosceles trapezoid. AD parallel to BC
ACCORDING TO THE QUESTION
75°+<B=180°
<B=180°-75°
<B=105°
Lenny has a model train layout on a large, rectangular board. The length, l, of the board is 3 times the width, w. Which equation can be used to find P, the perimeter of the board?
Answer:
8w
Step-by-step explanation:
Given that:
Length = l
Width = w
l = 3w
Perimeter of rectangular board :
Perimeter of a rectangle = 2(l + w)
Perimeter = 2(3w + w)
Perimeter = 2(4w)
Perimeter of rectangular board = 8w
5. Sand is dumped off a conveyor belt into a pile at the rate of 2 cubic feet per minute. The sand pile is shaped like a cone whose height and base diameter are always equal. At what rate is the height of the pile growing when the pile is 5 feet high? (The volume of a cone is fr2h where r is the radius of the base and h is the height:)
Answer:
[tex]\displaystyle \frac{dh}{dt} = \frac{8}{25 \pi} \ ft/min[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtract Property of EqualityGeometry
Volume of a Cone: [tex]\displaystyle V = \frac{1}{3} \pi r^2h[/tex]
r is radiush is heightDiameter: d = 2r
Calculus
Derivatives
Derivative Notation
Differentiating with respect to time
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
[tex]\displaystyle \frac{dV}{dt} = 2 \ ft^3/min\\b = h\\h = 5 \ ft[/tex]
Step 2: Rewrite Volume Formula
We need to rewrite the cone volume formula in terms of height h only.
Base b = diameter d of the circular base
Define: b = dSubstitute: b = 2rWe are given that the base of the cone is the same as the height.
Define: b = 2rSubstitute: h = 2rNow solve for height.
Divide 2 on both sides: h/2 = rRewrite expression: r = h/2Now find new volume formula.
Define [VC]: [tex]\displaystyle V = \frac{1}{3} \pi r^2h[/tex]Substitute: [tex]\displaystyle V = \frac{1}{3} \pi (\frac{h}{2})^2h[/tex]Exponents: [tex]\displaystyle V = \frac{1}{3} \pi (\frac{h^2}{4})h[/tex]Multiply: [tex]\displaystyle V = \frac{1}{12} \pi h^3[/tex]We now have the same volume formula in terms of height h only.
Step 3: Differentiate
Basic Power Rule: [tex]\displaystyle \frac{dV}{dt} = \frac{1}{12} \pi \cdot 3 \cdot h^{3-1} \frac{dh}{dt}[/tex]Simplify: [tex]\displaystyle \frac{dV}{dt} = \frac{1}{4} \pi h^{2} \frac{dh}{dt}[/tex]Step 4: Solve for height rate
Substitute: [tex]\displaystyle 2 \ ft^3/min = \frac{1}{4} \pi (5 \ ft)^{2} \frac{dh}{dt}[/tex]Isolate h rate: [tex]\displaystyle \frac{2 \ ft^3/min}{\frac{1}{4} \pi (5 \ ft)^{2}} = \frac{dh}{dt}[/tex]Exponents: [tex]\displaystyle \frac{2 \ ft^3/min}{\frac{1}{4} \pi (25 \ ft^2)} = \frac{dh}{dt}[/tex]Multiply: [tex]\displaystyle \frac{2 \ ft^3/min}{\frac{25}{4} \pi \ ft^2} = \frac{dh}{dt}[/tex]Divide: [tex]\displaystyle \frac{8}{25 \pi} \ ft/min = \frac{dh}{dt}[/tex]Rewrite: [tex]\displaystyle \frac{dh}{dt} = \frac{8}{25 \pi} \ ft/min[/tex]Here this tells us that the rate at which the height is moving at a rate of 0.101859 feet per minute.
Rauol measured the height of 12 different plants in his garden in April. He measured them again in June. What is the difference between the mean height in April and the mean height in June?
The question is incomplete. Here is the complete question.
Raoul measured the ehight of 12 different plants in his garden in April. He measured them again in June.
April Heights (in inches) 12 15 23 11 42 45 44 39 12 19 20 12
June Heights (in inches) 45 45 40 43 11 14 12 13 41 40 45 41
What is the difference between the mean height in April and the mean height in June?
Answer: The difference between means is 8.0
Step-by-step explanation: Mean is the average of a set of numbers.
It is calculated as:
[tex]\mu=\frac{\Sigma x}{n}[/tex]
where
x is the numbers in the set
n is how many numbers are there in the set
For heights in April, the mean is:
[tex]\mu_{1}=\frac{12+15+23+11+42+45+44+39+12+19+20+12}{12}[/tex]
μ₁ = 24.5
For heights in June, the mean os:
[tex]\mu_{2}=\frac{45+45+40+43+11+14+12+13+41+40+45+41}{12}[/tex]
μ₂ = 32.5
The difference between means:
μ₂ - μ₁ = 32.5 - 24.5 = 8.0
The difference between the mean height in April and in June is 8.0 inches.
I need help pls so I can get a good grade
Answer:
Step-by-step explanation:
C is the answer.
The line graph below shows the number of chocolate bars and ice lollies sold at a small shop over a year.
Pick the month below in which more ice lollies were sold than chocolate bars.
January
July
April
May
Answer:
July
Step-by-step explanation:
Month in which more ice lollies were sold than chocolate bars are: Jun, Jul, Aug
This means that from the answer options only July is valid.