Answer:
28:20
Step-by-step explanation:
you just multiply 5 by 4 because 20 divided by 4 is 5 and then multiply 7 by 4
Answer:
Let total students be ‘X’
No of girls = (X-20)
Girls/Boys=7/5=(X-20)/20
7(20) =5(X-20)
140=5X-100
5X=240
X = 240/5
X =48
So, Total Students are 48
No of girls = (X-20) = 48-20 = 28
Step-by-step explanation:
A person invests 1500 dollars in a bank. The bank pays 4% interest compounded
annually. To the nearest tenth of a year, how long must the person leave the money
in the bank until it reaches 1800 dollars?
Answer:
4.6 years
Step-by-step explanation:
We are to calculate the time in years.
The formula is given as:
t = ln(A/P) / n[ln(1 + r/n)]
Where:
A = Amount after t years = 1800
P = Initial Amount invested = 1500
r = Interest rate = 4%
n = Frequency at which the interest was compounded = Annually = 1
First, convert R percent to r a decimal
r = R/100
r = 4%/100
r = 0.04 per year,
Then, solve our equation for t
t = ln(A/P) / n[ln(1 + r/n)]
t = ln(1,800.00/1,500.00) / ( 1 × [ln(1 + 0.04/1)] )
t = 4.649 years
Approximately = 4.6 years
What is the approximate area of the circle shown?
Use 3.14 to approximate pi. Round your answer to the nearest whole
number
18 cm
Answer:
254 cm^2
Step-by-step explanation:
18/2 = radius = 9
9^2(Pi) = 254 cm^2
Answer:
254
Step-by-step explanation:
ARE THESE FUNCTIONS YES OR NO? PLS HELP ME
PLS HELP. URGENT!!!! I’ll give whatever points
Find the answer for m∠EFD
Given:
In triangle DEF, [tex]DE = EF[/tex] and [tex]m\angle 98^\circ[/tex].
To find:
The measure of angle EFD.
Solution:
In triangle DEF,
[tex]DE = EF[/tex] (Given)
It means triangle DEF is an isosceles triangle.
[tex]m\angle EDF=m\angle EFD[/tex] (Base angles of an isosceles triangle are equal)
Using angle sum property in triangle DEF, we get
[tex]m\angle DE F+m\angle EFD+m\angle EDF=180^\circ[/tex]
[tex]98^\circ +m\angle EFD+m\angle EFD=180^\circ[/tex]
[tex]2m\angle EFD=180^\circ-98^\circ[/tex]
[tex]2m\angle EFD=82^\circ[/tex]
Divide both sides by 2.
[tex]m\angle EFD=\dfrac{82^\circ}{2}[/tex]
[tex]m\angle EFD=41^\circ[/tex]
Therefore, the measure of angle EFD is 41 degrees.
don’t have a calculator
Answer:
2.8
Step-by-step explanation:
the dude on the top is right :D
i need help with this i don’t understand
Answer:
15
measure of third side is = 25^2 - 20^2
= 625 - 400
= 225
= √225
= 15
hope it helps
Solve each of the following equations. Show its set on a number line.
|4x-4(x+1)|=4
Pls answer immediately i'm giving 100 points!!!
Answer:
The solution set is all real numbers.
Step-by-step explanation:
Solve this equation, we have:
[tex]4x - 4/mleft(x + 1/mright) = 4 \\ (4x - 4x - 4) = 4 \\ ( - 4) = 4 \\ 4 = 4[/tex]
The final sentence is always true, The solution set is all real numbers.
Showing it in the number line in blue, we have:
if boards that usually cost $660 are selling at 1/6 less than the normal price, what is there price now? PLEASE ANSEWR TIMED!!!!
Answer:
$554.40
Step-by-step explanation:
Answer:
$110
Step-by-step explanation:
1/6 x 660
f(x)=2x^3+ax^2-37x-60
The binomial x-4 is a factor of f(x). Find the value of a.
Given:
The function is
[tex]f(x)=2x^3+ax^2-37x-60[/tex]
The binomial [tex]x-4[/tex] is a factor of f(x).
To find:
The value of [tex]a[/tex].
Solution:
If [tex]x-c[/tex] is a factor of f(x), then [tex]f(c)=0[/tex].
It is given that, [tex]x-4[/tex] is a factor of f(x), then [tex]f(4)=0[/tex].
We have,
[tex]f(x)=2x^3+ax^2-37x-60[/tex]
Substituting x=4, we get
[tex]f(4)=2(4)^3+a(4)^2-37(4)-60[/tex]
[tex]f(4)=2(64)+a(16)-148-60[/tex]
[tex]f(4)=128+16a-208[/tex]
[tex]f(4)=16a-80[/tex]
Now,
[tex]f(4)=0[/tex]
[tex]16a-80=0[/tex]
[tex]16a=80[/tex]
[tex]a=\dfrac{80}{16}[/tex]
[tex]a=5[/tex]
Therefore, the value of a is 5.
Name the angles and sides of each pair of triangles that are congruent.
Answer:
Step-by-step explanation:
Corresponding parts of congruent triangles are congruent
WX ≅ DC
XY ≅ CY
WY ≅ DY
∠WXY ≅ ∠DCY
∠XWY ≅ ∠CDY
∠WYX ≅ ∠DYC
please help if you can?
Answer and Step-by-step explanation:
The range would be [-5, 0]
This is because the points are included, and this is how far the graph's y-values go.
The range is based of the y-values of the graph, in which it looks for the greatest y value of the graph and the smallest y value of the graph.
#teamtrees #PAW (Plant And Water)
Find the value of x and justify your answer
Answer: your question was to say that you were in the person that was in park today and i got a hold on the door and I got it back to you in the park and then I saw you on the way to your house to see if I was going back to the school to go get home with me so so we could go do that
Step-by-step explanation:
Answer:
a.
2x+4x+3x=180 sum of interior angle of the triangle is 180
9x=180
x=180/9=20
b.
x-20+x+10+x-20=180sum of interior angle of the triangle is 180
3x-30=180
3x=180+30
x=210/3=70
c.x+10+x+20+x=180 linear pair
3x+30=180
3x=180-30
x=150/3=50
Mrs. Williams put $500 into a retirement account that earns 4% interest. How long will it take for there to be $3,500?
What is the A value?
What is the B value?
What is the equation and answer?
9514 1404 393
Answer:
A = 500
B = 1.04
49.6 years
Step-by-step explanation:
We assume your 'A' and 'B' refer to parameters in an exponential formula of the form ...
y = A·B^x
In this form, A is the initial investment value, $500. B is the growth factor, 1+4% = 1.04, assuming interest is compounded annually. We want to find x such that y=$3500.
3500 = 500·1.04^x . . . . . fill in known values
7 = 1.04^x . . . . . . . . . . . . . divide by 500
log(7) = x·log(1.04) . . . . . . take logarithms
x = log(7)/log(1.04) ≈ 49.61 . . . . divide by the coefficient of x
It will take about 49.6 years for there to be $3500 in Mrs. Williams's account.
Find each missing angle of the trapezoid
Answer:
∠J = 107°
∠K =107°
∠L = 73°
∠M = 73°
Step-by-step explanation:
Angle J + angle M = 180°
(10x - 33) + (4x+17) = 180
simplify:
14x -16 = 180
14x = 196
x = 14
∠J = 10(14) - 33 = 107°
∠M = 4(14) + 17 = 73°
A sweatshirt was on sale for 25% off the marked price. The sweatshirt regularly costs $55.00. What is the sale price of the sweatshirt? $
type your answer....
$41.25
workings:100%->$55.00
1%->$55.00÷100=$0.55
25%->$0.55×25=$13.75
100%-25%=75%
Price of sweatshirt during sale->75%->$55.00-$13.75=$41.25
help help i really need it asap
Answer: c
Step-by-step explanation:
Answer:
=0.017+0.00025
=0.01725
=1.725×10^-2
=C
Can someone help me asap
Answer:
75 degrees
Step-by-step explanation:
All the interior angles of a triangle add up to 180 degrees. Knowing this, we can construct the following equation:
180=65+40+x
180=105+x
Subtract both sides by 105
180-105=105+x-105
75=x
Therefore, angle C has a measure of 75 degrees.
I hope this helps!
2. A landscaper drew a scale drawing of a rectangular yard using the scale, , before beginning to work on the yard.(a) The landscaper plans to put a fence around the entire yard. How many meters of fencing does she need?
Complete question :
A landscaper drew a scale drawing of a rectangular yard using the scale, , before beginning to work on the yard.
(a) The landscaper plans to put a fence around the entire yard. How many meters of fencing does she need? Show your work.
(b) The landscaper plans to create a rectangular garden that is the size of the actual yard. What is the area of the garden?
Answer:
28cm ; 48cm²
Step-by-step explanation:
From the diagram :
Length = 8cm
Width = 6cm
Meters of fencing required :
Perimeter of rectangle :
P = 2(length + Width)
P = 2 (8cm + 6cm)
P= 2(14cm)
P = 28 cm
2.)
Area of rectangle :
Length * width
8cm * 6cm
= 48cm²
A rhombus has side of length 60 units each and the lengths of its perpendicular diagonals are in the ratio of 2 to 1. What is the area of the rhombus, in square units?
Answer:
2880 square units
Step-by-step explanation:
Since the area of a rhombus, A = d₁ × d₂/2 where d₁ and d₂ are its diagonals. Given that d₁:d₂ = 2:1, d₁/d₂ = 2/1, so d₁ = 2d₂. Also, the length of side of the rhombus L = 60 units.
We find the length of the diagonal by Pythagoras' theorem since the diagonals are perpendicular to each other and bisect each other at their mid point.
The mid point of d₁ = d₁/2 and the midpoint of d₂ = d₂/2.
By Pythagoras' theorem,
L² = (d₁/2)² + (d₂/2)²
L² = d₁²/4 + d₂²/4
Now, d₁ = 2d₂
So, L² = (2d₂)²/4 + d₂²/4
L² = 4d₂²/4 + d₂²/4
L² = d₂² + d₂²/4
L² = 5d₂²/4
d₂² = 4L²/5
taking square root of both sides,
√d₂² = √(4L²/5)
d₂ = 2L/√5
Since L = 60 units, then
d₂ = 2L/√5
d₂ = 2(60)/√5
d₂ = 120/√5
rationalizing the denominator by multiplying the numerator and denominator by √5, we have
d₂ = 120/√5 × √5/√5
d₂ = 120√5/5
d₂ = 24√5 units
So, our area A = d₁ × d₂/2
Since d₁ = 2d₂, our area is
A = 2d₂ × d₂/2
A = d₂ × d₂
A = d₂²
substituting d₂ = 24√5, we have
A = d₂²
A = (24√5)²
A = (24)²(√5)²
A = 576 × 5
A = 2880 square units
Andrew is paid £250 a week. Each week, he shares his pay with his sister in the ratio 3 : 2 saves 12% of his share. How many weeks will it take Andrew to save £360?
Answer:
20 weeks
Step-by-step explanation:
The computation of The number of weeks it will take to save £360 is shown below:
Now $250 should be divided into a ratio of 3:2
He keeps = 150
ANd, he gives her = 100
As he saves 12% of his share
i.e.
= 12% of 150
= 18
Now the number of weeks would be
= 360 ÷ 18
= 20 weeks
PLS HELP Select all the expressions that represent the total area of this rectangle.
Answer:
E and D
Step-by-step explanation:
The area of a rectangle is length x width. In this case, that's (12+s) x 1/3
This can be re-written as 1/3(12+s)
D is 1/3s + 4 which is what happens when you multiply 1/3 by 12 which = 4 and multiply 1/3 by s which = 1/3s. So the answer is 1/3s+4.
Which of these is the algebraic expression for "4 times the sum of 2 and y?"
a 4 ⋅ 2 + y
b 4(2 + y)
c 2 + 4 ⋅ y
d 2(4 + y)
Answer:
b
Step-by-step explanation:
The sum of 2 and y is 2 + y, then 4 times this sum is
4(2 + y) → b
Laney and Maka are tutors. Laney charges $10 for travel expenses plus $32 per hour of tutoring. The dollar amount Maka charges can be modeled by the equation F=30h+14, where h represents the number of hours that Maka tutors and F represents the total amount earned. What is the difference in the total amount Laney and Maka each charge for 4 hours of tutoring?
Answer: Total amount earned by Laney in 4hour=$138
Total amount earned by Maka in 4hours=$134
Difference =$4
Step-by-step explanation:
Since
Maka charges can be modeled by the equation F=30h+14,
where h =number of hours that Maka tutors
F = the total amount earned. Following same model
With 14 being the charge in dollar for travel expenses.
Laney charging $10 for travel expenses plus $32 per hour of tutoring can also be represented as
F= 32h +10
Such that total amount earned by
Maka in 4hours gives
F=30h+14
F=30x4 +14
F=120+14=$134
In the same vein the total amount earned by Laney in 4hours gives
F=32h+10
F= 32x4+10
F=128+10=$138
The difference in money earned by Laney and Maka = $138-$134= $4
Which type of transformation is shown?
Answer:
rotation? I think I'm not sure to or reflection
Answer:
rotation
Step-by-step explanation:
size, shape, and angle measures are preserved but orientation is not
Which answer choice best describes Saundra’s claim?
The surface area of this triangular pyramid whose bases and lateral faces are congruent equilateral triangles is
Answer:
The answer is below
Step-by-step explanation:
A triangular pyramid is a pyramid with a triangular base. It is a polyhedron (3 dimensional shape) composed of four triangular faces, six straight edges, and four vertex corners.
The surface area of a triangular pyramid with congruent equilateral triangles = 4 * area of one triangle
Area of one triangle = (1/2) * base * height = (1/2) * 15 in * 13 in = 97.5 in²
Surface area of pyramid = 4 * 97.5 in² = 390 in²
What is the measure of angle b?
Answer:
b=36
Step-by-step explanation:
by triangle exterior theorem
b+81 = 117
b=36
Answer:
B is 36 degrees, and a is 63 degrees
Step-by-step explanation:
180 - 117 = 63
a = 63 degrees
81 + 63 + b = 180
144 + b = 180
180 - 144 = b
36 degrees = b
Find the inverse equation of y=3x-12
Answer:
[tex]f {}^{ - 1}(x) = \frac{x}{3} + 4[/tex]
Step-by-step explanation:
[tex]y = 3x - 12[/tex]
Flip the variables then solve for y
[tex]x = 3y - 12[/tex]
[tex] \frac{x}{3} = y - 4[/tex]
[tex] \frac{x}{3} + 4 = y[/tex]
[tex]f {}^{ - 1} (x) = \frac{x}{3} + 4[/tex]
Mr. Wright needs to buy a water tank for his classroom. The tank must fit inside a storage box that is shaped like a cube with side lengths of 20 feet. Water tanks are available in cylinders, cones, square pyramids, and spheres. Mr. Wright wants to buy the tank that has the largest capacity… What shape should he buy?
Answer:
square pyramids
Step-by-step explanation:
Square pyramids because they have corners and the storage box is shaped like a cube. If he gets things with rounded edges, then there will be empty space between each water tank.