Answer:
2 balls/ft²
Step-by-step explanation:
The area of the gym is:
A = (100 ft) (60 ft)
A = 6,000 ft²
The population density is:
D = 12,000 balls / 6,000 ft²
D = 2 balls/ft²
Final answer:
To calculate the population density of balls in a gym, divide the total number of balls by the gym's area in square feet. In this case, with 12,000 balls and a gym of 6,000 square feet, the population density is 2 balls per square foot.
Explanation:
The question involves calculating the population density of balls in a gym. First, we need to find the area of the gym to understand the space these balls will occupy. The gym is 100 feet long and 60 feet wide, thus its area is 100 * 60 = 6,000 square feet.
Next, we're told there are 12,000 balls available in the gym. To find the population density of the balls, the number of balls is divided by the area of the gym. So, the population density is 12,000 balls divided by 6,000 square feet, which equals 2 balls per square foot.
Craig has the following data: 14,14,16,b,1 If the range is 25, what is the value of b?
Final answer:
The student needs to find the missing number 'b' in a data set, given that the range is 25. Since we know the smallest value is 1, adding the range to that value gives us the largest possible number, which in this case is 26. Therefore, 'b' must be 26 to achieve the specified range.
Explanation:
The student is asking about finding a missing value in a set of numbers given the range of the data set. To find the value of b, we must remember the definition of range: Range is the difference between the largest and smallest values in a set.
With the knowledge that the range is 25, and having the numbers 14, 14, 16, and 1, we identify 1 as the smallest value.
If we add the range to the smallest number (1 + 25), we get the largest number the set could contain, which is 26.
Since the other numbers in the set are all smaller than 26, b must equal 26 for the range to be 25.
Two fire trucks on the ground on either side of a burning building are 1.3 miles apart. They each measure the angle of elevation to the fire, which are 58 degrees and 52 degrees. How far is each truck from the fire. Step by step explanation.. Please..Thanks..
Answer:
A-0.5777miles
B-0.7223miles
Step-by-step explanation:
Let A be truck with 58°, B be truck with 52° elevation and C be the position of the fire. We know that the AB is 1.3 miles apart.
-Using sine rule, we find the length of AB and BC as:
[tex]\angle C=180-(58+52)=70\textdegree\\\\\frac{a}{sin \ A}=\frac{b}{sin \ B}=\frac{c}{sin \ C}\\\\\frac{1.3}{sin \ 70}=\frac{b}{sin \ 52}\\\\b=\frac{1.3 sin \ 52}{sin 70}=1.0902mi\\\\\\c=\frac{1.3 sin \ 58}{sin 70}=1.1732[/tex]
#Bisect angle C, and use sine rule again to find the lengths of bisected AB:
[tex]\frac{a}{sin \ A}=\frac{b}{sin \ B}=\frac{c}{sin \ C}\\\\\frac{1.0902}{sin \ 90}=\frac{x}{sin \ (90-58)}\\\\x=\frac{1.0902\ sin \ 32}{sin \ 90}=0.5777mi[/tex]
Truck B's position is calculated as 1.3mi-0.5777miles=0.7223miles
Hence, truck one is 0.5777miles and truck two is 0.7223 miles from the fire.
-6(1-3n) - 4n = -34 + 7n
The answer is n= -4. It shows the work to get -4
A triangle has side lengths of 11 inches, 15 inches, and 20 inches. Find the angle measures of the triangle. Round decimal answers to the nearest tenth.
Answer:
I don't know but I have the equations. (also Im going to assume you know a bit of trig)
Step-by-step explanation:
You have to use law of cosines.
a=11
b=15
take these equations and plug in the variables
a^2=b^2+c^2-2bc cos(a)
b^2=a^2+c^2-2ac cos (b)
c^2=a^2+b^2-2ab cos(c)
you will get something along the lines of
something=cos a
something=cos b
something=cos c
then in a calculator you push inverse cos or cos-1(x) and input the "something" into as x and that answer should be one angle, and repeat it for the rest of the three values.
Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.)
3 tan(θ) sin(θ) − 2 tan(θ) = 0
Answer:
Note from question, Let K be any integer. Integer = 1
θ = πk
θ = 3.142 * 1
θ = 3.142 in three decimal places
θ = sin⁻¹ (2/3) + 2kπ
θ = sin⁻¹0.667 + 2*1*3.142
θ = 0.718 + 6.284
θ = 7.002 in three decimal places
∴ 7.002 , 3.142
Step-by-step explanation:
Considering the equation
3 tan(θ) sin(θ) − 2 tan(θ) = 0
The objective is to solve the equation.
First solve the equation in one period.
3 tan(θ) sin(θ) − 2 tan(θ) = 0
( 3sinθ − 2 ) tanθ = 0
Therefore, 3sinθ − 2 = 0 also tanθ = 0
=> sinθ = 2/3 , tanθ = 0
Pick the right equation.
tanθ = 0
θ = tan⁻¹ 0
θ = 0
Using the unit circle, the period of tangent functions is π
Then the general solution of the equation is θ = 0 + πk ==> θ = πk
Pick the left equation.
3sinθ − 2 = 0
3sinθ = 2
sinθ = 2/3
θ = sin⁻¹ (2/3)
As the sine function has period 2π
Then the general solution is θ = sin⁻¹ (2/3) + 2kπ
What is the result when the number 22 is decreased by 9.1%?
Answer:
19.998
Step-by-step explanation:
Take the number and decrease (subtract) by 9.1% of the original number
22 - 22*9.1%
Change the percent to decimal form
22 - 22*.091
22 -2.002
19.998
Final answer:
The result when the number 22 is decreased by 9.1% is 20.0, after calculating 9.1% of 22, which is 2.002, and subtracting it from 22 and rounding to the nearest tenths place.
Explanation:
To find the result when the number 22 is decreased by 9.1%, you can use the following steps:
Calculate the decrease amount by finding 9.1% of 22: (9.1/100) × 22.
Subtract the decrease amount from the original number: 22 - (9.1% of 22).
Using a calculator, the decrease amount is:
(0.091) × 22 = 2.002.
Then subtract this from the original number:
22 - 2.002 = 19.998.
However, we need to report our final answer to the nearest tenths place since that is the precision of the number 9.1%. Therefore, we round 19.998 to 20.0 to reflect the proper significant figures.
So, the result when the number 22 is decreased by 9.1% is 20.0.
Solve: 4/3 x −4 = 5 + x A) 0.5 B) 2 C) 18 D) 27
Answer:
D) 27
Step-by-step explanation:
1. add 4 on both sides to leave 4/3x by itself
2. subtract x on both sides to cancel x on the right side
3. multiply 3 ton both sides to cancel out fraction
Answer:
d(27)
Step-by-step explanation:
What is the expression?
Answer: x + 4
5x
Step-by-step explanation:
The first one is "x + 4" because you are adding 4 to the 1st number
The second one is "5x" because you are multiplying 5 to the 2nd number.
Neil has 3 partially full cans of white paint . They contain 1/3 gallon , 1/5 gallon and 1/2 gallon of paint. About how many paint does Neil have in all
Answer:
31/30 gallons
Step-by-step explanation:
finding the lowest common denominator for all three numbers. so 1/3 becomes 10/30, 1/5 becomes 6/30, and 1/2 becomes 15/30. 10/30+6/30+15/30=31/30
Answer:31/30
Step-by-step explanation:
you have to first find a common denominator. Which in this case is 30 so then you have to multiply by the same number for both bottom and top number of the fraction. 1/3 = 10/30 1/5=6/30 1/2=15/30. Then, you just have to add JUST THE TOP NUMBERS. You get 31/30 then divide that and i will leave that last part to you. Hope this helps!
what is equivalent to 3/12 and 1/6
Answer:
1/4 and 2/12
Step-by-step explanation:
If you mulitply both the numerater and denominator by 2 (or any number) it will be equivelent.
1/6 is equivelient to 2/12, 3/18, etc.
However, if you divide 3/12, you get 0.25, which is equivelent to 1/4
Consider a distance and time graph whose y-axis is distance and x-axis is time. What do you know about a runner's motion at the time when a segment of the graph is horizontal?
a) The runner is moving at a steady rate.
b) The runner is slowing down.
c) The runner is speeding up.
d) The runner has stopped.
e) The runner is running very slowly
somebody pleaseee help its due in 9 mins
Answer:
the answer is d.) the runner stopped
Step-by-step explanation:
because the distance is staying the same but the time is changing wich means the runner isn't moving for a period of time.
In a study of crime, the FBI found that 13.2% of all Americans had been victims of crime during a 1-year period. This result was based on a sample of 1,105. Estimate the LOWER LIMIT of the confidence interval of the percentage of victims at the 99% confidence level.
Please round to the nearest whole number.
Answer:
11%
Step-by-step explanation:
The margin of error is the standard error times the critical value.
For a proportion, the standard error is:
σ = √(pq / n)
σ = √(0.132 × 0.868 / 1105)
σ = 0.0102
Since n is large, we can approximate the critical value using a normal distribution. For 99% confidence, the critical value is 2.576.
The margin of error is:
ME = 0.0102 × 2.576
ME = 0.026
The confidence interval is 0.132 ± 0.026. So the lower limit is 0.106, or 10.6%. Rounded to the nearest whole number, that's 11%.
How do I use successive approximations ?
Answer:
assume an approximate value for the variable that will simplify the equation.
solve for the variable.
use the answer as the second approximate value and solve the equation again.
repeat this process until a constant value for the variable is obtained.
2. What type of transformations moves P (3,-7) to P"(3,7)
Reflection
Rotation
Dilation
None of above
The type of transformation that moves P (3,-7) to P'' (3,7) is a reflection. The point has been flipped over the x-axis.
Explanation:The type of transformation which moves point
P (3,-7)
to
P'' (3,7)
is a
reflection
. It appears that point P has simply been flipped over the x-axis. The x-coordinate remains unchanged at 3, but the y-coordinate has been reflected to the opposite side of the x-axis, changing it from -7 to 7. So, a reflection over the x-axis is the correct transformation in this case. The transformation that moves point P (3,-7) to P'' (3,7) is a reflection over the x-axis. When a point is reflected in the x-axis, the y-coordinate changes sign while the x-coordinate remains the same. In this case, when the y-coordinate of P changes from -7 to 7, it means that P was reflected over the x-axis.
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If (x, y) is a solution to the system of equations, what is the value of y? 1/4 x + 1/8 y = 2 1/3 x + 1/2 y = 4 A) 4 B) 6 C) -6 D) -4
Solution:
Given system of equations are:
[tex]\frac{1}{4}x + \frac{1}{8}y =2 ---------- eqn\ 1\\\\\frac{1}{3}x + \frac{1}{2}y = 4 -------------- eqn\ 2[/tex]
We have to find value of y
From eqn 1,
[tex]\frac{1}{4}x + \frac{1}{8}y =2 \\\\2x + y = 2 \times 8\\\\2x + y = 16 ---- eqn\ 3[/tex]
From eqn 2,
[tex]\frac{1}{3}x + \frac{1}{2}y = 4\\\\2x + 3y = 4 \times 6\\\\2x + 3y = 24 ------ eqn\ 4[/tex]
Subtract eqn 3 from eqn 4
2x + 3y = 24
2x + y = 16
( - ) -----------------
2y = 8
y = 4
Thus value of y is 4
If you flip a coin and roll a
6-sided die, what is the probability that you will flip a heads and roll an even number?
Answer:
the answer is 1/4
Step-by-step explanation:
1/2 *3/6=1/4
a car rental company charges $75.00 rental fee plus $30.00 per day. Selena paid $225.00 to rent car
Answer:
5 days
Step-by-step explanation:
First subtract the flat fee so that you know you just have the price of the days
225-75
150 Then divide by 30, the day rate so you know how many days it was
150/30= 5
Selena had the car for 5 days
You want to buy 2 blue baseball caps which has a price tag of $30.50 each from Clovis's hat store, Of sales tax is 8.6 percent, how much will you pay for the two blue baseball caps?
Answer:
66.25
Step-by-step explanation:
30.50 times 2 is 61 that’s for two caps
61 times 1.086 (1 is for the amount you are actually going to pay .086 is what percent is because you have to move the decimal over two when you are changing percent to decimal) and that comes out to 66.246. you round the 4 to 5 to get to nearest cent and comes out to be 66.25
Answer: $66.25
Step-by-step explanation:
Two baseball cap at $30.5 each is $30.5 ×2 = $61
Sales tax at 8.6% = 8.6/ 100= 0.086
Sales tax = 0.086 × 61
= 5.246
Total amount to be paid = $66. 25
Is a temperature of -11 degrees warmer or colder than a temperature of -15 degrees? *
Answer:
warmer
Step-by-step explanation:
-11 is closer to zero the -15
Answer:
warmer
Step-by-step explanation:
-15 is colder.
Determine the center and radius of the following circle equation:
22 + y2 + 8x – 12y + 3 = 0
Please help :)
Answer:
center(8x,12y) radius 3
Step-by-step explanation:
If i am doing this correct
PLEASE HELP ME WITH THIS ASAP
Answer:
1900 ft
Step-by-step explanation:
To find the area where roses will be planted, find the area of the 2 triangles. 60×38 divided by 2 = 1140ft. 40×38 divided by 2 = 760. 760+1140=1900
each day alyssa jogs for 25 minutes on a treadmill she jogs 135 meters a minute at the speed at which alyssa is jogging how many centimeters does she jog each second
Answer: she is jogging 2.25 i think
Step-by-step explanation:
im sorry im not sure i just divided 135 by 60 but i dont think its right:(
Ty puts 9 Sports cards each on the front and back of each page in his cars album. How many pages are in Ty’s album if he has 144 cards?
SHOW WORK
grusi lob ze cruz?masi pa koi foitaitua leo leone fatua fatui?
A circle has a circumference of 150 meters. What is the measure of its radius? Round
to the nearest tenth.
circumference = 150 m
What is the measure of its radius?
Answer:
[tex]2\pi \times \: r = 150 \\ 6.2831r = 150 \\ \frac{6.2831r}{6.2831} = \frac{150}{6.2831} \\ r = 23.87cm[/tex]
Answer:
23.9
Step-by-step explanation:
circumference = Diameter · Pie
150 = X · pie
divide both sides by pie(use the accrual symbol on a calc) and you get 47.7 as the diameter then divide 47.7 by 2 and you get 23.9 as you radius
if £1 is 1.18 euros how much pounds will theo get if he has 407.10 euros
Answer:
345.
Step-by-step explanation:
Just divide 407.10 by 1.18 and you'll get your answer.
What is the quotient? 2 and one-fifth divided by negative StartFraction 1 over 10 EndFraction –22 Negative StartFraction 11 over 50 EndFraction StartFraction 11 over 50 EndFraction 22
Answer: i think the answer is -22 which is A
Step-by-step explanation:
Answer:
-22
Step-by-step explanation:
I put it in decimal form so it would be like this.2.20 dived by -.10 and got -22
At a pet store, the ratio of female birds to male birds was 7:4. Write a sentence explaining what this means.
Which is the length of the arc MPN expressed in terms of pie?
The arc MPN is a major arc, and the length of arc MPN is 79/9π
How to determine the arc length?The given parameters are:
Ф = 360 - 44
Radius, r = 5
The arc length is then calculated using:
[tex]L = \frac{\theta}{360} * 2\pi r[/tex]
So, we have:
[tex]L = \frac{360 - 44}{360} * 2\pi * 5[/tex]
[tex]L = \frac{316}{360} * 2\pi * 5[/tex]
Evaluate the product
[tex]L = \frac{3160}{360} \pi[/tex]
Divide
[tex]L = \frac{79}9 \pi[/tex]
Hence, the length of arc MPN is 79/9π
Read more about arc lengths at:
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What is 24+ 2X equals 31
First, subtract 24 from 31.
31 - 24 = 7
Now divide 7 by 2.
7 ÷ 2 = 3.5
Plug 3.5 into the equation to check.
24 + (3.5 × 2) = 31
x = 3.5
Alex is making puppets for a show. He bought all the string needed for $125.It costs $18 for the remaining materials to make each puppet. What is the total cost to make 50 puppets
Answer:
900
Step-by-step explanation:
ANSWER: y
=
125
+
900
50
=
$
20.5
Step-by-step explanation: Cost of each puppet =
$
20.5
Explanation:
The number of puppets :
50
-------(given)
Let cost of each puppet be
y
So, total cost will be
50
y
He brought all string needed for
$
125
He needs to invest
$
18
for EACH puppet for the remaining material, i.e.
18
×
50
=
$
900
is the total extra investment to be done.
So total cost will be :
125
+
900
=
50
y
#therefore cost of each puppet will be :