Final answer:
To find the number of girls and boys on the bus, create a system of linear equations and solve for the variables. In this case, there are 12 boys and 24 girls on the bus.
Explanation:
To solve for the number of girls and boys on the bus:
Let G represent the number of girls and B represent the number of boys.
From the problem, G = 2B and G + B = 36.
Substitute G = 2B into the second equation to get 2B + B = 36, which gives B = 12. Therefore, there are 12 boys and 24 girls on the bus.
Tim bought a soft drink for 2 dollars and 5 candy bars. He spent a total of 22 dollars. How much did the candy bar costs?
The figures in each pair are similar. Find the value of each variable. Show your work.
find the area of triangle QRS.
Answer: 140 square units.
Step-by-step explanation:
The area of triangle with vertices [tex](x_1,y_1),(x_2,y_2)\ and\ (x_3,y_3)[/tex] is given by
[tex]\text{Area}=\frac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2][/tex]
Then area of triangle QRS with vertices (6,10), (2,-10) and (-9,5) is given by :-
[tex]\\\\\Rightarrow\text{Area}=|\frac{1}{2}[6(-10-5)+2(5-10)-9(10-(-10))]|\\\\\Rightarrow\text{Area}=|\frac{1}{2}[6(-15)+2(-5)+-9(20)]|\\\\\Rightarrow\text{Area}=|\frac{1}{2}[280]|\\\\\Rightarrow\text{Area}=140\text{ square units}[/tex]
Answer:
the answer is 140. I did the assignment
An upscale resort has built its circular swimming pool around a central area that contains a restaurant. The central area is a right triangle with legs of 60 feet, 120 feet, and approximately 103.92 feet. The vertices of the triangle are points on the circle. The hypotenuse of the triangle is the diameter of the circle. The center of the circle is a point on the hypotenuse (longest side) of the triangle. The building permit the resort obtained requires that the resort state how much water the pool will hold so the city can manage the resort’s water rights effectively.
a.)What is the area of the largest section of the pool? Explain if you feel this area would be large enough to add a waterslide.
b.)How much water do you need to fill just the pool without the fish tank, if the average depth is 4 feet?
The largest section of the pool is 11307.2 square feet and it seems feasible to add a water slide based on this area. In order to fill the pool, considering that the average depth is 4 feet, approximately 338511.6 gallons of water would be needed.
Explanation:We will first find the area of the circular pool, keeping in mind that the hypotenuse of the triangle serves as the diameter. We will use the formula for the area of a circle, A = πr², where r is the radius of the circle. Here, the radius is half of the hypotenuse so it's 120 feet / 2 = 60 feet.
This makes the area of the circle A = π * 60² = 3600π square feet. This, minus the area of the triangle which can be calculated by (1/2) * base * height = (1/2) * 60 * 103.92 = 3117.6 square feet. So, the largest section of the pool is 3600π - 3117.6 = 11307.2 square feet.
Additional structures such as a water slide could be considered based on the remaining area. Due to size of the pool, it seems feasible to add a water slide without significantly disrupting the swimming space. However, additional calculations considering the base area of the slide would be required for a definitive answer.
The amount of water needed to fill the pool is calculated by multiplying the volume of the pool by the weight of the water. If the average depth of the pool is 4 feet, the volume of the pool (ignoring the central triangle) is 11307.2*4 = 45228.8 cubic feet. As 1 cubic foot of water equals roughly translates to 7.48 gallons, the pool would require approximately 45228.8 * 7.48 = 338511.6 gallons of water.
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Which term best describes a proof in which you assume the opposite of what you want to prove?
Answer:
Contradictory Statement
Step-by-step explanation:
In contradictory statement , we basically describes a proof by assuming opposite of what we want to prove .
For example :
Prove that [tex]\sqrt{2}[/tex] is irrational .
Solution :
We will prove this by contradiction .
Let if possible [tex]\sqrt{2}[/tex] is rational .
[tex]\sqrt{2}=\frac{p}{q}[/tex] where p and q are integers and coprime such that [tex]q\neq 0[/tex]
On squaring both sides , we get
[tex]2q^2=p^2\\\Rightarrow 2|p^2\\\Rightarrow 2|p[/tex]
we get ,
p=2r
On squaring both sides, we get
[tex]p^2=4r^2\\\Rightarrow 2q^2=4r^2\\\Rightarrow q^2=2r^2\\\Rightarrow 2|q^2\\\Rightarrow 2|q[/tex]
So, 2 divides p and q which is a contradiction to the fact that p and are coprime .
Therefore, [tex]\sqrt{2}[/tex] is irrational .
a tower casts a 450 ft shadow at the same time that a 4 ft child casts a 6 ft shadow. Write and solve a proportion to find the height of a tower
Answer:
[tex]x=300[/tex]
Step-by-step explanation:
Set up the proportion;
[tex]\frac{x}{450} =\frac{4}{6}[/tex]
then cross multiply;
[tex]6x=450[/tex] · [tex]4[/tex]
[tex]6x=1800[/tex]
[tex]x=\frac{1800}{6} =300[/tex]
[tex]x=300[/tex]
When simplified, the expression (x ^1/8) (x^3/8) is 12. Which is a possible value of x?
Draw a graph of the rose curve.
r = 2 sin 3θ, 0 ≤ θ ≤ 2π
determine which of the following logarithms is condensed correctly
Hillary age is 3 years greater than 2/3 times Lilly's age if Hillary is 19 years old how old is Lilly
Hillary = 3+2/3X
19=3+2/3X
16=2/3X
X= 16 / 2/3 = 16/1* 3/2 = 48/2
X=24
Lilly is 24
How many radians are contained in the angle AOT in the figure? Round your answer to three decimal places.
A. 0.459 radian
B. 2.178 radians
C. 1.047 radians
D. 0.955 radian
Answer:
Option C. 1.047 radians
Step-by-step explanation:
We have to find the measure of angle AOT in radians.
To convert measure of an angle from degree to radians we use the formula
[tex]\text{radians}=\frac{\pi(\text{degrees})}{180}[/tex]
= [tex]\frac{\pi(60)}{180}=\frac{\pi }{3}[/tex]
(Since measure of angle AOT is 60°)
= [tex]\frac{3.14}{3}[/tex] (since π = 3.14)
= 1.047 radians
Therefore, option C. 1.047 radians is the correct option.
Find all solutions in the interval [0, 2π).
sin^2 x + sin x = 0
what is the product? 3x^5 (2x^2+4x+1)
Answer:
The product of the given polynomial [tex]3x^5(2 x^2+4x+1)[/tex] is [tex]6x^7+12x^6+3x^5[/tex]
Step-by-step explanation:
Given: Polynomial [tex]3x^5(2 x^2+4x+1)[/tex]
We have to find the product of the given polynomial [tex]3x^5(2 x^2+4x+1)[/tex]
Consider the given polynomial [tex]3x^5(2 x^2+4x+1)[/tex]
Apply distributive rule, [tex]a(b+c)=ab+ac[/tex]
Multiply [tex]3x^5[/tex] with each term in brackets, we have,
[tex]=3x^5\cdot \:2x^2+3x^5\cdot \:4x+3x^5\cdot \:1[/tex]
[tex]=3\cdot \:2x^5x^2+3\cdot \:4x^5x+3\cdot \:1\cdot \:x^5[/tex]
Apply exponent rule, [tex]a^b\cdot \:a^c=a^{b+c}[/tex]
Simplify, we have,
[tex]=6x^7+12x^6+3x^5[/tex]
Thus, The product of the given polynomial [tex]3x^5(2 x^2+4x+1)[/tex] is [tex]6x^7+12x^6+3x^5[/tex]
He lake is 60 miles away, and rene is driving at 40 miles per hour the entire time, how long will it take her to get to the lake
divide distance by speed
60/40 = 1.5
it will take 1 1/2 hours ( 90 minutes)
rationalize the denominator. write it in simplest terms
3
------
√12x
x - 2(x + 10) = 12 what's x
9log9(4) =
A. 3
B. 4
C. 9
D. 81
Simplify
[tex] \frac{ \frac{1}{x+h} + \frac{1}{x} }{x} [/tex]
Sixty-five percent of men consider themselves knowledgeable football fans. if 12 men are randomly selected, find the probability that exactly four of them will consider themselves knowledgeable fans.
Answer:
P(x)= 0.0198
Step-by-step explanation:
Given : 65% men are knowledgeable football fans, 12 are randomly selected ,
To find : Probability that exactly four of them will consider themselves knowledgeable fans.
Solution : Let P is the success rate = 65% = 0.65
Let Q is the failure rate = 100-65= 35%= 0.35
Let n be the total number of fans selected = 12
Let r be the probability of getting exactly four = 4
Formula used : The binomial probability
[tex]P(x)= \frac{n!}{(n-r)!r!}P^rQ^{n-r}[/tex]
putting values in the formula we get ,
[tex]P(x)= \frac{12!}{(12-4)!4!}(0.65)^4(0.35)^{12-4}[/tex]
[tex]P(x)= (495)(0.1785)(o.ooo22 )[/tex]
P(x)= 0.0198
The probability that exactly four out of the twelve randomly selected men will consider themselves knowledgeable football fans is approximately 0.236 or 23.6%.
Step 1: Model Selection (Binomial Distribution)
This scenario can be modeled using the binomial distribution if the following conditions are met:
Fixed number of trials (n): In this case, we have a fixed number of men being selected (n = 12).Binary outcome: Each man can be classified into two categories: either a "knowledgeable fan" (success) or a "not knowledgeable fan" (failure).Independent trials: The knowledge level of one man doesn't affect the selection of another.Constant probability (p): The probability (p) of a man being a knowledgeable fan remains constant throughout the random selection (given as 65%).Since these conditions seem reasonable, the binomial distribution is a suitable model for this scenario.
Step 2: Formula and Values
The probability (P(x)) of exactly x successes (knowledgeable fans) in n trials (men selected) with probability p of success (knowledgeable fan) can be calculated using the binomial probability formula:
P(x) = nCx * p^x * (1 - p)^(n-x)
where:
n = number of trials (12 men)x = number of successes (4 knowledgeable fans - what we're interested in)p = probability of success (knowledgeable fan - 65% converted to decimal: 0.65)(1 - p) = probability of failure (not knowledgeable fan)Step 3: Apply the Formula
We are interested in the probability of exactly 4 men being knowledgeable fans (x = 4). Substitute the known values into the formula:P(4) = 12C4 * 0.65 ^ 4 * (1 - 0.65) ^ (12 - 4)Step 4: Calculate Using Calculator or Software
While it's possible to calculate 12C4 (combinations of 12 choosing 4) by hand, using a calculator or statistical software is often easier.12C4 = 495 (combinations of 12 elements taken 4 at a time)Step 5: Complete the Calculation
Now you have all the values to complete the calculation:P(4) = 495 * 0.65 ^ 4 * (1 - 0.65) ^ 8Using a calculator or software, evaluate the expression. You'll get an answer around 0.236.The function f(x) = –x2 + 28x – 192 models the hourly profit, in dollars, a shop makes for selling sodas, where x is the number of sodas sold and f(x) is the amount of profit. Part A: Determine the vertex. What does this calculation mean in the context of the problem? (5 points) Part B: Determine the x-intercepts. What do these values mean in the context of the problem? (5 points)
In a random sample of 75 individuals, 52 people said they prefer coffee to tea. 99.7% of the population mean is between 84/80/74 % and 64/58/54%. (Choose the option closest to your answer.)
Rectangle R has varying length l and width w but a constant perimeter of 4 ft. A. Express the area A as a function of l. What do you know about this function? B. For what values of l and w will the area of R be greatest? Give an algebraic argument. Give a geometric arguement.
Approximately 7% of people are left-handed. if two people are selected at random, what is the probability of p(one is right-handed and the other is left-handed)
The required probability that one is right-handed and the other is left-handed is 217/1650.
Given that,
Approximately 7% of people are left-handed. if two people are selected at random, what is the probability of p(one is right-handed and the other is left-handed) is to be determined.
What is probability?
Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
Total number of left-handed people out of 100 = 7
Total number of right-handed people out of 100 = 100 - 7 = 93
Now,
Probability of picking 2 person(one is right-handed and the other is left-handed) = 7 / 100 (93/99) = 217/1650.
Thus, the required probability that one is right-handed and the other is left-handed is 217/1650.
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How can you use a number line to compare and order numbers?
A rectangular picture frame measures 4.0 inches by 5.5 inches. To cover
the picture inside the frame with glass costs $0.99 per square inch.
What will be the cost of the glass to cover the picture?
area = 4 x 5.5 = 22 square inches
cost is 0.99 per sq. inch
22 * 0.99 = 21.78
cost is $21.98
To find the cost of the glass for a 4.0 inch by 5.5 inch picture frame, calculate the frame's area and multiply it by the cost per square inch. The glass would cost $21.78.
To calculate the cost of the glass needed to cover the picture, you first need to determine the area of the glass required. The frame measures 4.0 inches by 5.5 inches, so the area can be found using the formula for the area of a rectangle, which is length multiplied by width.
The area is therefore 4.0 inches × 5.5 inches = 22.0 square inches. With the cost of glass being $0.99 per square inch, the total cost can be calculated by multiplying the area of the glass by the cost per square inch:
Total cost = 22.0 square inches × $0.99/square inch = $21.78.
Therefore, the cost of the glass to cover the picture would be $21.78.
Factor the expression
4b^2+28b+49
A herd of 39 horses has 33 white horses some black horses. What is the ratio of black horses to white horses?
There is 6 black horses, so 6/39.
06.01 LC)
Four graphs are shown below:
Which graph represents a positive nonlinear association between x and y?
Graph A
Graph B
Graph C
Graph D
Answer:
d
Step-by-step explanation:
help help help help help please
Solve the inequality.