Answer: 14
Step-by-step explanation:
The number of fraternity members taking physics but not mathematics is 27, calculated using inclusion-exclusion principle: 18 members take math, 5 take both math and physics, and 8 take neither.
Let's use the principle of inclusion-exclusion to solve this problem.
Total fraternity members (n) = 40
Members taking mathematics (M) = 18
Members taking both mathematics and physics (B) = 5
Members taking neither mathematics nor physics (N) = 8
To find the number of members taking physics but not mathematics (P).
We can start by using the formula for the number of elements in the union of two sets:
n(M ∪ P) = n(M) + n(P) - n(B)
Since the total members are 40, the equation becomes:
18 + n(P) - 5 = 40
Solving for n(P):
n(P) = 40 - 18 + 5
n(P) = 27
Therefore, 27 members take physics but not mathematics.
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Use the Pythagorean Theorem to find the missing side. Round your answer to the nearest hundredth.
19 m
52 m
Answer:
55m
Step-by-step explanation:
a²+b²=c²
19 x 19 = 361
52 x 52 = 2704
2704 + 361= 3065
the square root of 3065 is 55.4 so round that to 55.
If f(x) = -3x – 9 and g(x) = (x+7,
what is (fºg)(-6)?
Helppp
Answer:
-12
Step-by-step explanation:
we know that
(fºg)(x)=f(g(x))
To find out the composite function f(g(x)) substitute the variable x in the function f(x) by the function g(x)
we have
[tex]f(x)=-3x-9[/tex]
[tex]g(x)=x+7[/tex]
so
[tex]f(g(x))=-3(x+7)-9[/tex]
For x=-6
substitute
[tex]f(g(-6))=-3(-6+7)-9[/tex]
[tex]f(g(-6))=-3(1)-9[/tex]
[tex]f(g(-6))=-12[/tex]
You start driving north for 21 miles, turn right, and drive east for another 20 miles.
How many miles must you travel to return directly back to your starting point?
Answer:
40
Step-by-step explanation:
add 21 + 20
hope this helps :)
What's the distance between (–4, 3) and (4, 3)?
Answer:
The distance between (-4, 3) and (4, 3) is 8
Step-by-step explanation:
Distance formula: [tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2)}[/tex]
Distance: [tex]\sqrt{(4 - (-4)^2 + (3 - 3)^2}[/tex]
Distance: [tex]\sqrt{(4 + 4)^2 + (0)^2}[/tex]
Distance: [tex]\sqrt{8^2} \\[/tex]
Distance: 8
Answer: The distance between (-4, 3) and (4, 3) is 8
The lid of a jewelry box is in the shape of a triangular prism. The lid has a height of 10 inches. The triangular base of the lid has a base of 6 1/2 inches and a height of 3 1/2 inches. What is the volume of the lid to the nearest tenth?
The volume of the lid is approximately 113.8 cubic inches.
Explanation:The volume of the lid can be found by multiplying the area of the triangular base by the height of the lid. The area of a triangle can be found by using the formula: Area = (base x height) / 2. In this case, the base is 6 1/2 inches and the height is 3 1/2 inches. Plugging these values into the formula, we get: Area = (6.5 x 3.5) / 2 = 11.375 square inches. Now, to find the volume of the lid, we multiply the area by the height: Volume = 11.375 x 10 = 113.75 cubic inches. Rounding to the nearest tenth, the volume of the lid is 113.8 cubic inches.
The volume of the lid is 113.8 cubic inches.
To determine the volume of the lid of the jewelry box, we need to use the formula for the volume of a triangular prism, which is V = (1/2 * base * height of triangular base) * height of the prism.
First, calculate the area of the triangular base:
Base of the triangular base: 6.5 inchesHeight of the triangular base: 3.5 inchesArea = 1/2 * 6.5 inches * 3.5 inches = 11.375 square inchesNext, multiply the area of the triangular base by the height of the prism:
Height of the prism: 10 inchesVolume = 11.375 square inches * 10 inches = 113.75 cubic inchesTherefore, the volume of the lid to the nearest tenth is 113.8 cubic inches.
Find two numbers, if
Their sum is − 1/3 and their difference is 18
Let the two numbers be [tex]x,y[/tex].
We have
[tex]\begin{cases}x+y=-\frac{1}{3}\\x-y=18\end{cases}[/tex]
From the second equation, we derive [tex]x=18+y[/tex]
Plugging this value in the first equation, we have
[tex]18+y+y=-\dfrac{1}{3} \iff 2y=-\dfrac{1}{3}-18\iff 2y=-\dfrac{55}{3} \iff y=-\dfrac{55}{6}[/tex]
And we derive
[tex]x=18+y=18-\dfrac{55}{6}=\dfrac{53}{6}[/tex]
Answer:
The two numbers are: -9.17 and 8.83
Step-by-step explanation:
Let the two numbers represent 'x' and 'y'
Their sum is − 1/3 ==> x + y = -1/3 .................(eqn 1)
Their difference is 18 ==> x − y = 18 ....................(eqn 2)
from equation 2,
x = 18 + y
therefore, substitute for 'x' in (eqn 1) to get y
(18+y) + y = -1/3
18 + 2y = -1/3
2y = -1/3 − 18
2y = -[tex]18\frac{1}{3}[/tex]
2y = - 55/3
y = (-55/3) / 2
y = -55/3 x 1/2
y = -55/6 = -9.17
Substitute for 'y' in either equation
picking (eqn 2)
x − (-9.17) = 18
x + 9.17 = 18
x = 18 − 9.17
x = 8.83
KNOWLEDGE CHECK: ALEKS
The value of x that satisfies the equation 41 - x = 157 is x = -116.
To solve for x in the equation 41 - x = 157, we need to isolate x on one side of the equation.
Let's go step by step:
Step 1: Start with the given equation.
41 - x = 157
Step 2: Get rid of the constant term on the left side (41) by subtracting it from both sides of the equation.
(41 - x) - 41 = 157 - 41
Simplifying the left side:
41 - 41 - x = 157 - 41
0 - x = 116
Step 3: We have -x on the left side, and we want to solve for x, so we need to get rid of the negative sign in front of x.
To do that, we can multiply both sides of the equation by -1.
When we multiply a number by -1, the sign changes.
(-1) * (-x) = (-1) * 116
Simplifying the left side:
x = -116
Step 4: Now we have found the value of x, which is x = -116.
To verify our solution, we can substitute the value of x back into the original equation and see if it holds true:
41 - (-116) = 157
Simplifying:
41 + 116 = 157
157 = 157
Since both sides of the equation are equal after simplification, our solution x = -116 is correct.
Therefore, the value of x that satisfies the equation 41 - x = 157 is x = -116.
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Spinning Spinner 1st Simulation Colors Tally red 14 yellow 6 green 19 blue 1 2nd Simulation Colors Tally red 24 yellow 17 green 28 blue 11 3rd Simulation Colors Tally red 26 yellow 24 green 32 blue 38 Jill conducted three simulations of spinning a fair spinner (four sections of different colors--red, blue, yellow, green). The first simulation consisted of 40 spins, the second simulation consisted of 80 spins and the third simulation consisted of 120 spins. The results were recorded in the tables shown. Do the results for the green section follow the law of large numbers? Why or why not? A) no, because the probability of green is the same for each of the simulations. B) yes, because the probability of green is different for each of the simulations. C) no, because with each simulation, as the number of trials increase, the probabilities vary greatly and do not approach the theoretical probability of 1 4 . Eliminate D) yes, because with each simulation, as the number of trials increase, the experimental probability gets closer and closer to the theoretical probability of 1 4 .
Answer: D
Step-by-step explanation: yes, because with each simulation, as the number of trials increase, the experimental probability gets closer and closer to the theoretical probability of
1/4.
The answer is D
Step-by-step explanation:
because with each simulation, as the number of trials increase, the experimental probability gets closer and closer to the theoretical probability of
1
4
. The law of large numbers indicates that if an event of probability p is observed repeatedly during independent repetitions, the ratio of the observed frequency of that event to the total number of repetitions approaches p as the number of repetitions becomes arbitrarily large.
A cable television provider offers six
different news stations. If 25% of the
stations offered are news, how many
stations are offered by the provider?
Answer:
24 stations
Step-by-step explanation:
we know that
six stations represent 25% of the stations offered
so
using a proportion
Find out how many stations represent a percentage of 100%
[tex]\frac{6}{25\%}=\frac{x}{100\%}\\\\x=6(100)/25\\\\x=24\ stations[/tex]
You need 2 gallons of juice for every 12 people attending the open house. How many gallons of juice would be needed for 156 people?
Answer:
26 gallons of juice
Step-by-step explanation:
156/12 = 13
13x2=26
Answer: 26 gallons
Step-by-step explanation:
2 gallons for every 12 people so you want to do 156 divided by 12 which would be 13. That shows that there are 13 times more people than there were before. You would then multiply 2 by 13 which would give you 26 gallons of juice.
multiply 72 x 25/100
Answer:
18
Step-by-step explanation:
Answer:
18
Step-by-step explanation:
What is the decimal equivalent of the rational number -1/8
Answer:
-0.125
Step-by-step explanation:
To find the decimal version of the fraction, divide using a calculator or long division.
-1 / 8 = -0.125
Best of Luck!
Answer these 2 questions and you get 15 points
Question 1: Option B: [tex]\frac{10}{14}=\frac{5}{7}[/tex]
Question 2: Option C: [tex]\frac{12}{18}=\frac{4}{6}[/tex]
Solution:
Question 1:
Given ratio is [tex]\frac{10}{14}[/tex].
To find the equivalent ratio of [tex]\frac{10}{14}[/tex].
10 and 14 have the common factor 2.
So divide both numerator and denominator by the common factor 2.
[tex]$\frac{10}{14}=\frac{10\div2}{14\div 2}[/tex]
[tex]$=\frac{5}{7}[/tex]
[tex]$\frac{10}{14}=\frac{5}{7}[/tex]
Hence option B is the correct answer.
Question 2:
Given ratio is [tex]\frac{10}{14}[/tex].
To find the equivalent ratio of [tex]\frac{12}{18}[/tex].
12 and 18 have the common factor 3.
So divide both numerator and denominator by the common factor 3.
[tex]$\frac{12}{18}=\frac{12\div3}{18\div 3}[/tex]
[tex]$=\frac{4}{6}[/tex]
[tex]$\frac{12}{18}=\frac{4}{6}[/tex]
Hence option C is the correct answer.
HELP PLEASE BE QUICK
Answer:
Option A, V = π(7)^2h
Step-by-step explanation:
The formula for the volume of a cylinder: V = πr^2h
Step 1: Since the give us diameter we need to find radius
radius = diameter/2
radius = 14/2
radius = 7
Answer: Option A, V = π(7)^2h
Answer:
A
Step-by-step explanation:
Volume of a cylinder = pi r2 h
Where pi = 3.14
Radius r = diameter/2
Diameter given is 14,
So radius = 24/2 = 7
Height h
Volume = pi(7)^2 h
The length of a rectangle is 2 units more than the width. The area of the rectangle is 48 units. What is the width, in units, of the rectangle?
Final answer:
To find the width of a rectangle when the length is 2 units more than the width and the area is known to be 48 units, you can use algebraic equations to determine the width. In this case, the width of the rectangle is 6 units.
Explanation:
To find the width of the rectangle:
Let x be the width of the rectangle.
Since the length is 2 units more than the width, the length is x + 2.
Given that the area is 48 units, use the formula for the area of a rectangle: width x length = area. Therefore, x(x + 2) = 48.
Solve for x by setting up the equation: x^2 + 2x - 48 = 0.
Factor the quadratic equation: (x + 8)(x - 6) = 0.
Since the width cannot be negative, the width of the rectangle is 6 units.
The width of the rectangle is 6 units.
According to the question, the length is 2 units more than the width, so we can express the length as ( w + 2 ) units.
The area of a rectangle is given by the product of its length and width. Therefore, we can set up the following equation to represent the area of the rectangle:
[tex]\[ \text{Area} = \text{length} \times \text{width} \] \[ 48 = (w + 2) \times w \][/tex]
Expanding the right side of the equation, we get:
[tex]\[ 48 = w^2 + 2w \][/tex]
To find the value of w, we need to solve the quadratic equation. Let's rearrange the equation to set it equal to zero:
[tex]\[ w^2 + 2w - 48 = 0 \][/tex]
Now, we can factor this quadratic equation:
[tex]\[ (w + 8)(w - 6) = 0 \][/tex]
Setting each factor equal to zero gives us two possible solutions for w:
[tex]\[ w + 8 = 0 \quad \text{or} \quad w - 6 = 0 \][/tex]
Solving for w, we get:
[tex]\[ w = -8 \quad \text{or} \quad w = 6 \][/tex]
Since the width of a rectangle cannot be negative, we discard the negative solution. Therefore, the width of the rectangle is:
[tex]\[ w = 6 \text{ units} \][/tex]
the equation of a line β is 2x-3y=6
find the gradient of β
Answer:
2/3
Step-by-step explanation:
Rewrite the equation into the form of y=mx+c
m is the gradient of the line.
2x-3y=6
3y= 2x-6 (bring y terms to one side, the rest to the other)
y= 2/3x -2 (÷3 throughout)
Thus the gradient is 2/3.
7 + 7x; 7(x+1)
Are these equivalent?
TRUE or FALSE?
Answer:
I believe it would be true
find the equation of the tangent to the curve at x=3 for parametric equations
x = t + 1/t
y = t^2 + 1/(t^2) when t is greater than 0
Answer:
y = 6x − 11
Step-by-step explanation:
x = t + (1/t), y = t² + (1/t²)
If we square x:
x² = t² + 2 + (1/t²)
x² = y + 2
When x = 3, y = 7.
Taking derivative with respect to time:
2x = dy/dx
dy/dx = 6
So the equation of the tangent line is:
y − 7 = 6 (x − 3)
y − 7 = 6x − 18
y = 6x − 11
how do i find the area of this stop sign using subtraction?
Answer:
745.12
Step-by-step explanation:
30 x 30 = 900 which is the sign if it were a square
then you subtract the four corner pieces
900 - 4([tex]\frac{1}{2}[/tex](8.8 x 8.8))
900 - 2(77.44)
900 - 154.88
= 745.12
The length and width of a rectangle are 4 feet and 3 feet, respectively. A similar rectangle has a length of 10 feet. What is the width of the second rectangle?
A trapezoid was made by joining a pentagon and a triangle. the dimensions of the trapezoid are- height: 1 feet, bases 1/2 feet and 1 1/2 feet. the dimensions of the triangle are- height: 1/2 feet, base 1/2 feet. what is the area of the pentagon
Answer
3
Step-by-step explanation:
the formulas say it
A 23-year-old female buys 25/50/100 liability insurance, collision insurance with a $250 deductible, and comprehensive insurance with a $100 deductible. What is her total annual premium? Use the base premium and rating factor tables used to calculate the annual car insurance premium of a person.
Answer: $1090.80
Step-by-step explanation:
Answer:
$1,090.80
Step-by-step explanation:
Bodily injury; 25/50=$220
Property; 100=$375
Collision deductibles;$250=$185
Comprehensive deductibles;$100=$129
220+375+185+129 = 909
909*1.2=1,090.8
Took the test
Jorge is setting up his tent. He is using two nylon ropes to pull the tent taut and stabilize it at each end. If the tent is 5 feet tall, and Jorge stakes the ropes into the ground 3 feet from the tent, what is the total length of nylon rope he will use, to the nearest tenth of a foot? Show all of your work. PLEASE HELP ME !!!!!!!!!!
Answer: 5.8 ft
Step-by-step explanation:
We can use the Pithagorean Theorem in this problem, in order to find the length of the rope:
[tex]h^{2}=a^{2}+b^{2}[/tex]
Where:
[tex]h[/tex] is the length of the rope (the hypotenuse of the right triangle formed by the height of the tent, the rope and the ground)
[tex]a=5 ft[/tex] is the height of the tent (one of the legs of the right triangle)
[tex]b=3 ft[/tex] is the other leg of the right triangle
Solving the equation with the given data:
[tex]h^{2}=5^{2}+3^{2}[/tex]
Finding [tex]h[/tex]:
[tex]h=\sqrt{(5 ft)^{2}+(3 ft)^{2}}[/tex]
[tex]h=\sqrt{25 ft+9 ft}[/tex]
[tex]h=5.83 ft \approx 5.8 ft[/tex] This is the total length of nylon rope
A farm stand wants to sell fruit to local grocery stores in packages with
baskets of grapes, worth $5 apiece, and baskets of plums, worth $10 apiece.
The owner wants each package to include 35 baskets total, and he wants to
sell each package for $290. How many baskets of grapes and how many
baskets of plums should he put in each package?
O
A. 12 grapes, 23 plums
OB. 10 grapes, 5 plums
O
C. 5 grapes, 10 plums
O
D. 23 grapes, 12 plums
A.12 grapes, 23 plums
Step-by-step explanation:
1. solve all the equations by multiplying each number by how much each item is worth
2. A: 290 =(12× 5)+(10×23)
B: 100 =(10×5)+(5×10)
C:125 =(5×5)+(10×10)
D:235 =(23×5)+(12×10)
Evaluate 60 • x-60 · 15, when x=8.
Step 1 60• x-60 • 15 = 60(x - 15)
Step 2
Step 3
= 480 – 15
Step 4
465
Where is the error
Answer:
The right answer is, -420
Step-by-step explanation:
Because we use common factor:
60 (x - 15)
We multiply for each term:
60 (x) - 60 (15)
60 (8) - 60 (15)
We solve:
480 - 900 = -420
At his last track meet, Eli ran the 400-meter dash in 54 seconds. His friend Kimberly bet him that he couldn't run a whole kilometer at that pace, but Eli is determined to prove her wrong. How many minutes would he have to run at this pace to win the bet?
Write your answer as a whole number, decimal, or simplified fraction. Do not round.
Answer:
Eli has to run for 2.25 minutes at this pace to win the bet.
Step-by-step explanation:
At his last track meet, Eli ran the 400-meter dash in 54 seconds.
So, the speed of Eli's run is [tex]\frac{400}{54} \times 60 = 444.44[/tex] meters per minute.
Now, if Eli is determined to run a whole kilometer with the same speed, then it will take Eli to run 1 kilometer within [tex]\frac{1000}{444.44} = 2.25[/tex] minutes.
Hence, Eli has to run for 2.25 minutes at this pace to win the bet. (Answer)
If h = 24 units and r = 8 units, what is the volume of the cone shown above?
Use 3.14 for π
Answer:
1,607 volume
Step-by-step explanation:
help please, ive been sitting on this chair for 2 hours
Answer:
Step-by-step explanation:
We need to analyze the surface
Look at the L shape, it has a mirror image at the back, which is symmetrical to the front side
Then,
area of rectangle = length × breadth
The L shape can be divided into two plane shape
1. A rectangle of length 10in and breadth 6in,
Then, A=l×b=10×6 = 60in²
2. To a square of side a=4in
Then, A=s²=4²=16in²
Then, the total area of one side of the L shape is
A=60+16=76in²
Also, the total area of the two L shape is =2×76
A=152in²
Then, let look at the back side of the solid and the front side, they are also symmetrical.
It forms a rectangle of length 10in and breadth 6in
Then, A= l×b=10×6=60in²
Area of the two sides is =60×2
A=120in²
The total are of the front and back side is 120in²
A=120in²
Let take a look at the top and bottom, they are also symmetrical and has a dimension of length 10in and breadth 6in
Then, A=l×b=10×6=60in²
So, total area =2×60 =120in²
The total area of the shape is the total area of top+ total are of the sides + total area of the L shape
Total area=152+120+120=392in²
A(total)=392in²
Then, the total area of the solid shape is 392in²
The first option is correct
I need help please and can you explain
ANSWER ASAP!!!!
The app uses 2^28 bytes.
Step-by-step explanation:
Step 1: Given total storage used by the app = 4^4 Megabytes. Also, 1 MB = 2^20 bytes. Find total storage used by app in bytes.⇒ 4^4 × 2^20 = (2²)^4 × 2^20 = 2^8 × 2^20
= 2^8+20
= 2^28 bytes (using the law of exponents a^m × a^n = a^m+n)
In ΔGHI, the measure of ∠I=90°, the measure of ∠G=21°, and GH = 31 feet. Find the length of IG to the nearest tenth of a foot.
Answer:
[tex]IG=28.9\ ft[/tex]
Step-by-step explanation:
we know that
In the right triangle GHI
[tex]cos(G)=\frac{IG}{GH}[/tex] ----> by CAH )adjacent side divided by the hypotenuse)
substitute the given values
[tex]cos(21^o)=\frac{IG}{31}[/tex]
solve for IG
[tex]IG=cos(21^o)(31)=28.9\ ft[/tex]
see the attached figure to better understand the problem
Answer:
24.6
Step-by-step explanation: