Answer:
The maximum number of people that can be in the Trumpington marching band is 940 people
Step-by-step explanation:
The number of members = 20·n
The number per row = 26
The number left = 4
Therefore, we have;
If there are x rows of 26, we have;
26 × x = 20·n - 4
We have;
26 × x < 996
26 × x < 20·n
20·n < 996 therefore, 20·n ≤ 980
We check that 980/26 = 37 and some fractions
26 × 37 = 962 which will leave a remainder of 2
Therefore, we note that for 26 to have a remainder of 4, the last digit of the factor x must be 6 so has to get the last digit of the product 26 × x to be 6 while the digit of the product 20×n is 0 which will live 4 members out to get to the next 10 as follows;
26 × 36 = 936 while 20 × 47 = 940
We get 940 - 936 = 4 members
Therefore, the maximum number of people that can be in the Trumpington marching band = 940.
Get this correct i will give u brainliest.
Answer:
x = - 2, y = - 8
Step-by-step explanation:
Given the 2 equations
13x - 6y = 22 → (1)
x = y + 6 → (2)
Substitute x = y + 6 into (1)
13(y + 6) - 6y = 22 ← distribute and simplify left side
13y + 78 - 6y = 22
7y + 78 = 22 ( subtract 78 from both sides )
7y = - 56 ( divide both sides by 7 )
y = - 8
Substitute y = - 8 into (2) and evaluate for x
x = - 8 + 6 = - 2
Thus x = - 2, y = - 8
Use slope-intercept form, y = mx + b, to find the value for the y-intercept (b) of a line that has a slope of 6 and passes through the point (3, –5)
Answer:
y=6x-23
Step-by-step explanation:
-5=6(3)+b
-5=18+b
b=-23
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Answer:
6x-23
Step-by-step explanation:
Find the distance of (2,5) and (-1,3)
Answer:
[tex]\sqrt{13}[/tex]
Step-by-step explanation:
Use the distance formula:
[tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}[/tex]
Insert the values:
[tex](2_{x1},5_{y1})\\\\(-1_{x1},3_{y2})\\\\\\sqrt{(-1-2)^2+(3-5)^2}[/tex]
Simplify:
[tex]\sqrt{(-1-2)^2+(3-5)^2}\\\\ \sqrt{(-3)^2+(-2)^2}\\\\ \sqrt{9+4}\\\\\sqrt{13}[/tex]
The distance between the two points is the square root of 13.
:Done
Answer: [tex]\sqrt{13}[/tex] or 3.61
Step-by-step explanation:
[tex]\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]
[tex]\sqrt{\left(-1-2\right)^2+\left(3-5\right)^2}[/tex]
[tex]\sqrt{9+4}[/tex]
[tex]=\sqrt{13}[/tex]
5 times the quantity 7 minus a number f in an algebraic expression.
Answer:
(5*7)-f
Step-by-step explanation:
Algebraic expression for the given statement is [tex]5 \cdot 7 -f[/tex]
Algebraic expressionAlgebraic expression is the combination of terms that consists of numbers and variables connected by arithmetic operators.
Given statement is 5 times the quantity 7 minus a number f in an algebraic expression.
We need to write it in an algebraic expression
5 times a quantity. for product we use multiplication sign
For addition we use + sign and for difference we use minus sign .
5 times the quantity 7 means 5 multiplied by 7
[tex]5 \cdot 7[/tex]
5 times the quantity 7 minus a number f
subtract f from the expression we got
[tex]5 \cdot 7 -f[/tex]
Algebraic expression for the given statement is [tex]5 \cdot 7 -f[/tex]
Learn more information about 'Algebraic expression ' here:
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Can someone please help? the answer is 5/12 but I have no idea how. Please explain the steps!
Answer:
5/12
Step-by-step explanation:
4√y√y / 3√y
The above equation can be simplified as follow:
4√y√y / 3√y
4√y × √y ÷ 3√y
Recall:
√a = a^1/2
m√a = a^1/m
Therefore,
4√y√y ÷ 3√y
y^1/4 × y^1/2 ÷ y^1/3
Recall:
a^m × a^n = a^(m+n)
Therefore,
y^1/4 × y^1/2 ÷ y^1/3
y^(1/4 + 1/2) ÷ y^1/3
y^3/4 ÷ y^1/3
Recall:
a^m ÷ a^n = a^(m–n)
Therefore,
y^3/4 ÷ y^1/3
y^(3/4 – 1/3)
y^5/12
Comparing the above with y^m, we have
y^5/12 = y^m
m = 5/12
Therefore, the value of m is 5/12
5. The volleyball team has a double-header on Friday. The probability that they
will win both games is 38%. The probability that they will win just the first game is
70%, What is the probability that the team will win the second game given that
they have already won the first game?
Answer: 54.29%
Step-by-step explanation:
Given: The probability that they will win both games is 38%.
i.e. P( both games will win) =0.38
The probability that they will win just the first game is 70%.
P(first game will win) = 0.70
To find : P(second game will win| first game will win)
Using formula: [tex]P(B|A)=\dfrac{P(\text{both A and B})}{P(A)}[/tex]
So, P(second game will win| first game will win) = [tex]\dfrac{\text{ P( both games will win)}}{\text{P(first game will win)}}[/tex]
[tex]=\frac{0.38}{0.70}\approx0.5429=54.29\%[/tex]
Hence, the required probability = 54.29%
2x squared minus 1 equals 21
Answer:
x = √11
Step-by-step explanation:
2x² - 1 = 21
add 1 to both sides
2x² - 1 + 1 = 21 + 1
simplify
2x² = 22
x² = 22 / 2
x = √11
Answer:
x = √11
Step-by-step explanation
2x² - 1 = 21
negative sign crossing an equal to sign becomes a positive sign
2x² - 1 = 21 + 1
2x² = 22
x² = 22 / 2
x = √11
67) Interest on a Loan: Jeff Hubbard borrowed $800 from his brother for 2 years. At the end of 2 years, he repaid
the $800 plus $128 in interest. What simple interest rate did he pay?
Answer:
0.08%
Step-by-step explanation:
2 years,
the $800 plus $128 in interest. What simple interest rate did he pay?
128/2
$64 a year
64/800=0.08
so 0.08%
Myra wants to practice the piano for at least 22 minutes each day. Which of the following inequalities represents the number of minutes Myra will practice piano?
Answer:
[tex]x\geq 22[/tex]
Step-by-step explanation:
If someone wants to practice for at least 22 minutes a day, they want to practice 22 minutes or more. This is the same as greater than or equal to, and we want the minutes practices to be greater than or equal to 22. We can assume minutes practiced is x, and create the inequality [tex]x\geq 22[/tex].
Hope this helped!
a circular hall has a hemispherical roof. the greatest height is equal to the internal diameter .if the capacity of the hall is 43510 m^3 ,then the area of the floor is
This building is basically a cylinder with a hemisphere on top. Let d be the diameter of the hemispherical roof. This is also the height of the entire building as the greatest height is this value (which is located at the center of the building)
The hemisphere itself is r = d/2 meters high, which is the radius of the roof. The cylinder portion's height must be d - r = d - d/2 = 2d/2 - d/2 = d/2 = r meters. So basically the cylinder and the hemisphere both have the same height of r.
At the same time, the cylinder and hemisphere also have the same radius r, or else the roof wouldn't fit on the cylinder.
------------------------------
Volume of cylinder = pi*r^2*h = pi*r^2*r = pi*r^3
Note how I replaced h with r and simplified.
Also,
Volume of hemisphere = (1/2)*(volume of sphere)
Volume of hemisphere = (1/2)*( (4/3)*pi*r^3 )
Volume of hemisphere = (2/3)*pi*r^3
------------------------------
Add the two volume expressions
total volume = (volume of cylinder) + (volume of hemisphere)
total volume = (pi*r^3) + ( (2/3)*pi*r^3 )
total volume = (3/3)pi*r^3 + (2/3)pi*r^3
total volume = (5/3)pi*r^3
------------------------------
Set this equal to 43510 and solve for r
(5/3)pi*r^3 = 43510
pi*r^3 = (3/5)*43510
pi*r^3 = 26106
r^3 = 26106/pi
r = (26106/pi)^(1/3)
r = 20.2549023450428
The building has a radius of approximately 20.2549023450428 meters
------------------------------
We can now compute the area of the circular floor
area = pi*r^2
area = pi*(20.2549023450428)^2
area = 1,288.87316044698
Answer: approximately 1288.87316044698 square metersRound this however you need to
Which number is equal to 10^-3?
-1,000
-30
0.001
0.003
Work Shown:
10^(-3) = 1/( 10^3 ) = 1/1000 = 0.001
The rule used here is x^(-k) = 1/( x^k )
Answer:
C. O.001
Step-by-step explanation:
10^-3 = (1)/(10^3)
move the negative exponent to the denominator
(1)/(1000)
simplify 10^3 in the denominator
(1)/(1000) = 0.001
Polygons EFGH and E'F'G'H' are shown on the following coordinate grid:
hy
What set of transformations is performed on EFGH to form E'F'G'H'?
Answer:
A translation 3 units to the right and a 90-degree clockwise rotation
Step-by-step explanation:
An isosceles triangle has a vertex angle of 26°. Two sides of the triangle are each 15 ft long. Find the area of the triangle. A. 9.931 sq ft B. 98.629 sq ft C. 45.543 sq ft D. 49.314 sq ft
Answer:
D. 49.314 ft²
Step-by-step explanation:
Area = 1/2 s² sinФ
= 1/2 * 15² * sin(26)
= 49.314 ft²
How do you figure out the answer to this sum ???20x48
Answer:
Step-by-step explanation:
20
×48
-------
160
800
---------
960
Hope this helps
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Answer:
960Step-by-step explanation:
20×48 =
= 20×(40+8) =
= 20×40 + 20×8 =
= 2×4×100 + 2×8×10 =
= 800 + 160 =
= 960
Or:
20×48 = 2×48×10 = 96×10 = 960
Examine the table of input (x) and output (y) values below. What is the relationship between the input and output values? Write an equation for this relationship. input (x) –1 0 1 2 3 4 5 output (y) –4 –1 2 5 8 11 14 What do you notice about the relationship between the x and y values?
Answer:
Relationship: As the input increases by 1, the output increases by 3.
Equation: y=3x-1
~Hope this helps~
23. (a) The area of a rhombus is 90 cm. If the length of a diagonal is 18 cm. calculate the length of the
other diagonal
(b) The diagonals of a rhombus are 28 cm and 24 cm. Find the area of the rhombus.
10) () The height of a trapezium is 12 cm. Find the sum of its parallel sides if its area is 210 cm.
(ii) If the longer side is 2 times the length of the shorter side. find the length of the longer side.
Answer:
Step-by-step explanation:
a) area of rhombus = 1/2 × d1 × d2 = 90cm^2
here d1 and d2 are the diagonals
d1 = 18 cm
1/2 × 18 × d2 = 90
9 × d2 = 90
d2 = 90/9
d2 = 10 cm
∴The length of other diagonal is 10 cm
b) d1 = 28 cm
d2 = 24 cm
area = 1/2 × d1 × d2
= 1/2 × 28 × 24
= 336 cm^2
∴ The are of the rhombus = 336 cm^2
Hope this helps
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Which of the following lengths and widths represents a rectangle whose diagonal is rational? Question 3 options: length = 2, width = 1 length = 4, width = 4 length = 3, width = 2 length = 4, width = 3
Answer:
Correct option is length = 4, width = 3.
Step-by-step explanation:
Given:
Diagonal of a rectangle is rational.
To find:
Which of the following length and width options represent a rectangle ?
options:
length = 2, width = 1
length = 4, width = 4
length = 3, width = 2
length = 4, width = 3
Solution:
First of all, let us consider a rectangle as shown in the attached answer image.
Rectangle ABCD.
Width of rectangle is AB.
Width of rectangle is BC.
And the diagonal AC or BD can be found by using Pythagorean Theorem:
[tex]\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow AC^{2} = AB^{2} + BC^{2}\\\Rightarrow Diagonal^{2} = Length^{2} + Width^{2}[/tex]
Now, let us find diagonal for each option and check whether it is rational or not.
Option 1:
length = 2, width = 1
[tex]Diagonal^{2} = 2^{2} + 1^{2}\\\Rightarrow Diagonal^{2} = 5\\\Rightarrow Diagonal = \sqrt5[/tex]
Not rational
Option 2:
length = 4, width = 4
[tex]Diagonal^{2} = 4^{2} + 4^{2}\\\Rightarrow Diagonal^{2} = 32\\\Rightarrow Diagonal = 4\sqrt2[/tex]
Not rational.
Option 3:
length = 3, width = 2
[tex]Diagonal^{2} = 3^{2} + 2^{2}\\\Rightarrow Diagonal^{2} = 13\\\Rightarrow Diagonal = \sqrt{13}[/tex]
Not rational.
Option 4:
length = 4, width = 3
[tex]Diagonal^{2} = 4^{2} + 3^{2}\\\Rightarrow Diagonal^{2} = 25\\\Rightarrow Diagonal = \sqrt{25} = 5[/tex]
Diagonal is rational.
Correct option is length = 4, width = 3.
Select the equivalent expression.
C, because we multiply the exponents to get the answer.
Answer:
C
Step-by-step explanation:
Using the rule of exponents
[tex](a^{m}b^{n}) ^{p}[/tex] = [tex]a^{mp}[/tex] × [tex]a^{np}[/tex]
Thus
[tex](7^{2}5^{6})^4[/tex]
= [tex]7^{2.4}[/tex] × [tex]5^{6.4}[/tex]
= [tex]7^{8}[/tex] × [tex]5^{24}[/tex] → C
Find the slope of the line passing through the points (-9, -3) and (7,-7).
DI
DD
Undefined
$
?
Answer:
-1/4
Step-by-step explanation:
Slope = y/x - y1/x1
=> -7/7 - (-3/-9)
=> -7 +3 / 7+9
=> -4/16
=> -1/4
The slope for the given coordinates of points is -1/4.
What is the slope of straight line?The slope of a straight line is the tangent of the angle formed by it with the positive x axis as the reference.
The negative slope indicates the rate of decrease while the positive shows the rate of increase.
The given points are (-9, -3) and (7,-7).
The general expression to find the slope for two points (x₁, y₁) and (x₂, y₂) is given as,
m = (y₁ - y₂)/(x₁ - x₂)
Plug (x₁, y₁) = (-9, -3) and (x₂, y₂) = (7, -7) to get,
⇒ m = (-3 + 7)/(-9 - 7)
⇒ -1/4
Hence, the slope is obtained as -1/4.
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What is the (10) for?
Answer:
2(10) is implied multiplication
Step-by-step explanation:
( 18+2) + 2(10) ÷4 -2
PEMDAS
Parentheses first
( 20) + 2(10) ÷4 -2
Then exponents ( we have none)
Then multiply and divide from left to right
20 + 20÷4 -2
20 + 5-2
Then add and subtract from left to right
25 -2
23
2(10) is implied multiplication
Answer:
23
Step-by-step equation
(18+2)+2(10)÷4-2
20+20÷4-2
20+5-2
25-2
23
A right triangle has one angle that measure 23o. The adjacent leg measures 27.6 cm and the hypotenuse measures 30 cm. What is the approximate area of the triangle? Round to the nearest tenth. Area of a triangle = One-halfbh 68.7 cm2 161.8 cm2 381.3 cm2 450.0 cm2
Answer:
161.8 cm²
Step-by-step explanation:
The given formula works if you have both legs of the triangle. Using the given information, a better formula is ...
A = (1/2)ab·sin(C) . . . . C is the angle between sides 'a' and 'b'
A = (1/2)(27.6 cm)(30 cm)sin(23°) ≈ 161.8 cm²
Answer:
B on edg 2020
Step-by-step explanation:
Just took test
It is 8th grade math please get it right. My Dad gave this to me
Answer:
A=535.93
Step-by-step explanation:
A=P(1+r)^t
A=500[(1+0.07/4)]^4
A=535.93
solve for y. -y/3 = -23 simplify your answer as much as possible
Answer:
69
Step-by-step explanation:
-y/3 = -23
=> -y = -23 x 3
=> -y = -69
=> y = 69
Answer:
69
Step-by-step explanation:
We multiply both sides of the equation by 3 to cancel out the denominator. That gives us -y=-69. Since we cannot have a negative variable, we change the values on both sides, giving us y=69
Distance between the two points ? (-3,10) and (3,-2)
Answer:
Approximately 13.4 units.
Step-by-step explanation:
To find the distance between two points, use the distance formula. The distance formula is:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
x₁ and y₁ is one coordinate while x₂ and y₂ is the other.
Let (-3,10) be x₁ and y₁ and let (3,-2) be x₂ and y₂. Plug in the numbers and simplify:
[tex]d=\sqrt{(3-(-3))^2+(-2-10)^2}\\ d=\sqrt{6^2+(-12)^2} \\d=\sqrt{36+144} \\d=\sqrt{180}\\ d=\sqrt{36\cdot5}=6\sqrt{5}\approx13.4164[/tex]
Edit: Typo
Answer:
100
Step-by-step explanation:
I WILL GIVE U BRAINLIST AND A THANK YOU PLS ANDWER!!!!!!!!!
Answer:
yes it is proportional because you don't buy the popcorn
Answer:
A. Yes.
Step-by-step explanation:
Since you never buy popcorn, the only thing you buy are movie tickets. The only thing contributing to the total price are the movie tickets, so the total price is proportional to the number of movie tickets purchased.
Hope this helps!
What collateral secures a mortgage?
O A.
5% of the purchase price of the house
B.
the house itself
C.
10% of the purchase price of the house
D.
none
Answer:
The House
Step-by-step explanation:
If a TV set is bought on the installment plan there is a down payment of $25 and 12 monthly payments of $15 each. The same set may be bought for cash at 12% less than the installment price. The amount saved by making a cash payment is:
Answer:
Amount saved by making a cash payment is $24.6
Step-by-step explanation:
We start by calculating the amount to be paid if payment was by installments.
We are told that there would be a down payment of $25 and $15 every month for 12 months.
So total installment payment would be;
$25 + 12($15) = $25 + $180 = $205
Now let’s try and figure out the cash payment
For the cash payment, we have 12% less than installment payment.
Kindly note that 12% is same as 12/100 = 0.12
Thus, 12% less payment would be;
205-0.12(205) = 205 - 24.6 = $180.4
Thus, the amount saved if payment was cash would be;
$205 - $180.4 = $24.6
After taking off from the landing pad, a helicopter flies 3 miles west, then 2 miles southeast. How far is the helicopter from the landing pad? If someone could explain to that would be very helpful
Answer:
When the plane makes its turn to fly southeast, it makes a 45º angle at point a, making angle abc also equal to 45º.
Line ab is the 2 miles southeast the plane flies.
Line ac = line cb
sine (45º) = opposite / hypotenuse = cb / 2
.70711 = cb / 2
cb = 1.41422 miles = line ac
Line cs = 3 - 1.41422 = 1.58578
Line x^2 = cs^2 + cb^2
Line x^2 = 2.5146982084 + 2.0000182084
Line x^2 = 4.5147
Line x = 2.1248
Step-by-step explanation:
write -7.08 as a mixed number or fraction in a simplest from
Answer:
7 2/5
Step-by-step explanation:
7.08 to improper fraction:
708/100
= 7 2/25
If EH = 80, calculate GF.
Answer:
The length of Segment GF is 120
Step-by-step explanation:
Given that EH = 80, and AB, GF, RH, and DI are parallel lines, we have;
DC ≅ DE ≅ EF ≅ FA Given
Therefore, CI ≅ HI ≅HG ≅ GB (Triangle proportionality theorem)
From where we have;
EH/GF =CH/CG (Intercept theorem otherwise known as Thales' theorem )
CH = 2 × CI (Transitive property of equality)
Also CG = 3 × CI (Transitive property of equality)
EH/GF = 2×CI/(3×CI) = 2/3
EH/GF = 2/3
80/GF = 2/3
Therefore we have;
Segment GF = 80 × 3/2 = 120
The length of Segment GF = 120.
120 U-U
Mostly cuz i looked it up and i am not explaining it cuz i dont wanna
