Answer:
3.64 Km.
Step-by-step explanation:
Given,
Total population = 20,000 people
Population density = 480 people per square kilometer
Area of the circle town
[tex]A = \dfrac{20000}{480}[/tex]
[tex]A = 41.667\ km^2[/tex]
Radius of the circle town
[tex]\pi r^2 = 41.667[/tex]
[tex]r = 3.64\ km[/tex]
Hence, the radius of circle town is equal to 3.64 Km.
Answer:
3.64
Step-by-step explanation:
A person on a moving sidewalk travels 56 feet in 8 seconds. The moving sidewalk has a length of 140 feet. How long will it take to move from one end to the other?
Answer:
The answer is : 20 seconds
Step-by-step explanation:
First, we are told that it takes the person 8 seconds to travel 56 feet, hence, we will find the time it takes to travel one foot.
56 feet = 8 seconds
∴ 1 foot = 8/56 seconds
Next, we are told that the length of the sidewalk is 140 feet, therefore walking from one end of the sidewalk to the other is the the same as walking 140 feet, and this is calculated thus:
1 foot = 8/56 seconds (calculated above)
∴ 140 feet = 8/56 × 140 = 20 seconds
which expressions are equivalent ? A. 3v+5-9v+2 and 6v+6 B. -6n+3-2n+2 and -8n+6 C. -4n+8+9n-2 and 5n+6 D. 10n-5-2n+3 and 5n-2
Answer:
C. -4n+8+9n-2 and 5n+6
Step-by-step explanation:
The equivalent expression is found by combining like terms:
-4n +8 +9n -2 = n(-4+9) +(8-2)
-4n +8 +9n -2 = 5n +6 . . . . . matches choice C
__
The other answer choices have flaws in the work:
A. 3v -9v ≠ 6v
B. +3 +2 ≠ +6
D. 10n -2n ≠ 5n
Answer:
C. -4n+8+9n-2 and 5n+6
Step-by-step explanation:
Hope this helps, and holy cow! the person above me deserves brainliest!
Elena divided a decimal by a whole number. 84.36 ÷ 12 = ? Part A: Explain each step needed to divide 84.3y by 12. Part B: What is the correct qoutient?
Answer:
Part A. [tex]\frac{84.3y}{12} = 7 +\frac{0.1\cdot y}{4}[/tex]
Part B. The correct quotient is (3 × 4)
Step-by-step explanation:
Part A.
To divide 84.36 by 12 we look for the Highest Common Factor of the whole number and the decimal portions of the numerator and the denominator individually as follows;
[tex]\frac{84.36}{12} = \frac{84+0.3636}{12} = \frac{2 \times 2 \times 3 \times 7+0.01\times 12\times 3}{12} = \frac{12 \times 7+0.03\times 12}{12}[/tex]
Therefore, dividing 84.36 by 12 gives [tex]\frac{12 \times 7+0.03\times 12}{12} = 7+0.03[/tex] = 7.03
When dividing 84.3·y by 12, therefore, we have;
[tex]\frac{12 \times 7+0.3\times y}{12} = 7 +\frac{0.1\cdot y}{4}[/tex]
Part B.
The correct quotient should have factors of the numerator
Therefore the divisor 12 should be represented as follows
[tex]\frac{12 \times 7+0.3\times y}{12} =\frac{12 \times 7+0.3\times y}{3 \times 4}[/tex]
The correct quotient therefore = (3 × 4)
Elena divided the decimal 84.36 by the whole number 12 to get the correct quotient of 7.03. The division process is similar to dividing whole numbers but includes placing the decimal point correctly in the quotient.
To answer the question, Elena divided a decimal by a whole number. Specifically, the division problem is 84.36 ÷ 12. Dividing a decimal by a whole number follows the same process as dividing two whole numbers, with the additional step of placing the decimal point in the quotient.
Set up the division problem with 84.36 inside the division bracket and 12 on the outside.
Start dividing from the left. 12 goes into 84 seven times (12 x 7 = 84), so put 7 above the 84 in the quotient.
Subtract 84 from 84, which leaves 0, and bring down the next digit, which is 3 (from the decimal part).
Since 12 does not go into 3, we place a 0 in the quotient above the 3 and bring down the next digit, which is 6.
Now we have 36. 12 goes into 36 three times (12 x 3 = 36), so place a 3 in the quotient above the 36.
Again, we subtract 36 from 36, leaving 0, with no more digits to bring down, so we have our answer.
The correct quotient is 7.03. Multiplying or dividing by powers of ten, as seen when working with decimals, involves shifting the decimal point. For example, when multiplying 45.86 by 100, you would move the decimal point two places to the right, giving 4586. Conversely, dividing 1.9436 by powers of 10 shifts the decimal point to the left. The significance of this process is underlined by the fact that in scientific fields, calculations often require adjusting the decimal by powers of ten to maintain precision and correct significant figures.
It should be noted that a calculator provides the raw numerical result of a division and doesn't account for the significant figures involved; therefore, it's essential to consider how many decimal places are appropriate for the situation.
A toy company is considering a cube or sphere-shaped container for packaging a new product. The height of the cube would equal the diameter of the sphere . Compare the volume to surface area ratios of the containers. Which packaging will be more efficient? For a sphere, SA =4πr²
Answer:
Packaging with cube will be more efficient.
Step-by-step explanation:
Given:
A cube and a sphere where the diameter of the sphere is equal to the height of the cube.
Let the height of the cube "x"
Radius of the sphere = [tex](\frac{x}{2})[/tex]
Formula to be used:
Surface area of the cube = [tex]6x^2[/tex] and Surface area of the sphere = [tex]4\pi (r)^2[/tex]
Volume of the cube = [tex]x^3[/tex] and Volume of the sphere = [tex]\frac{4\pi r^3}{3}[/tex]
We have to compare the ratio of SA and Volumes.
Ratio of SA : Ratio of their volumes :
⇒ [tex]\frac{SA\ of\ cube\ (S_1)}{SA\ of\ sphere\ (S_2)}[/tex] ⇒ [tex]\frac{Volume \ of \ cube\ (V_1)}{Volume\ of\ sphere\ (V_2)}[/tex]
⇒ [tex]\frac{6x^2}{4\pi (\frac{x}{2})^2}[/tex] ⇒ [tex]\frac{x^3}{\frac{4 \pi r^3}{3} }[/tex]
⇒ [tex]\frac{6x^2}{4\pi (\frac{x^2}{4})}[/tex] ⇒ [tex]\frac{x^3}{\frac{4 \pi (\frac{x}{2})^3}{3} }[/tex]
⇒ [tex]\frac{6x^2}{\pi x^2}[/tex] ⇒ [tex]\frac{x^3}{\frac{4 \pi (\frac{x^3}{8})}{3} }[/tex]
⇒ [tex]\frac{6}{\pi}[/tex] ⇒ [tex]\frac{6}{\pi}[/tex]
⇒ approx [tex]2[/tex] ⇒ approx [tex]2[/tex]
⇒ [tex]S_1=2S_2[/tex] ⇒ [tex]V_1=2V_2[/tex]
Packaging of the toy with the cube will be more efficient as it has more volume comparatively.
Tyler went to an electronics store with a gift card. After he spent 13/20 of the gift card's value on a video game, the card's value was less than $26.25. Which inequality describes x, the value of the gift card when Tyler entered the store?
Answer:
[tex]\frac{7}{20}x < 26.25[/tex]
Step-by-step explanation:
If $x is the value of the gift card when Tyler entered the store, then after spending [tex]\frac{13}{20}[/tex] of the gift card the card's value was less than $26.25.
So, we can write the inequality as
[tex]x - \frac{13}{20}x < 26.25[/tex]
⇒ [tex]\frac{7}{20}x < 26.25[/tex]
So, this is the required inequality that describes x, the value of the gift card when Tyler entered the store. (Answer)
HELPPPP!!!!
Need the answer ASAP!!
Given that the functions [tex]f(x)=x+4[/tex] and [tex]g(x)=x^{3}[/tex]
We need to determine the value of the function [tex](g \ {\circ} f)(-3)[/tex]
First, we shall determine the composition of the function [tex](g \circ f)(x)[/tex]
Function [tex](g \circ f)(x)[/tex]:
Let us determine the function [tex](g \circ f)(x)[/tex]
Thus, we have;
[tex](g \circ f)(x)=g[f(x)][/tex]
[tex]=g[x+4][/tex]
[tex]=(x+4)^3[/tex]
[tex](g \circ f)(x)=x^3+3x^2(4)+3x(4)^2+(4)^3[/tex]
[tex](g \circ f)(x)=x^3+12x^2+48x+64[/tex]
Thus, the function is [tex](g \circ f)(x)=x^3+12x^2+48x+64[/tex]
Value of the function [tex](g \ {\circ} f)(-3)[/tex]:
The value of the function can be determined by substituting x = -3 in the function [tex](g \circ f)(x)=x^3+12x^2+48x+64[/tex]
Thus, we have;
[tex](g \circ f)(-3)=(-3)^3+12(-3)^2+48(-3)+64[/tex]
Simplifying the terms, we get;
[tex](g \circ f)(-3)=-27+12(9)+48(-3)+64[/tex]
[tex](g \circ f)(-3)=-27+108-144+64[/tex]
[tex](g \circ f)(-3)=1[/tex]
Thus, the value of the function [tex](g \ {\circ} f)(-3)[/tex] is 1.
Juan has $2,224.52 in his checking account that charges a $23 per check overdraft
protection fee. In the next 4 days, the following checks arrived from payment in the
following order: check 129 for $1,520.00, check 126 for $750.89, and check 127 for $185.00.
How much does Juan have in his account?
Answer: good luck
Step-by-step explanation:
The ages of students in a school are normally distributed with a mean of 15 years and a standard deviation of 2 years. Approximately what percent of the students are between 14 and 18 years old?
We have been given that the ages of students in a school are normally distributed with a mean of 15 years and a standard deviation of 2 years.
We are asked to find the percentage of students that are between 14 and 18 years old.
First of all, we will find z-score corresponding to 14 and 18 using z-score formula.
[tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]z=\frac{14-15}{2}[/tex]
[tex]z=\frac{-1}{2}[/tex]
[tex]z=-0.5[/tex]
Similarly, we will find the z-score corresponding to 18.
[tex]z=\frac{18-15}{2}[/tex]
[tex]z=\frac{3}{2}[/tex]
[tex]z=1.5[/tex]
Now we will find the probability of getting a z-score between [tex]-0.5[/tex] and [tex]1.5[/tex] that is [tex]P(-0.5<z<1.5)[/tex].
[tex]P(-0.5<z<1.5)=P(z<1.5)-P(z<-0.5)[/tex]
Using normal distribution table, we will get:
[tex]P(-0.5<z<1.5)=0.93319-0.30854[/tex]
[tex]P(-0.5<z<1.5)=0.62465[/tex]
Let us convert [tex]0.62465[/tex] into percentage.
[tex]0.62465\times 100\%=62.465\%\approx 62.5\%[/tex]
Therefore, approximately [tex]62.5\%[/tex] of the students are between 14 and 18 years old.
Answer:
62.47%
Step-by-step explanation:
The cost of 4 ice cream cones from the snack bar was $10.40. If each ice cream cone costs the same amount, which model correctly illustrates the relationship? Check all that apply.HELPPPP
y = 10.4 x
y = 2.6 x
y = 4 x
Cost of Ice Cream Cones
A 2-column table with 3 rows. Column 1 is labeled number of ice cream cones with entries 13, 26, 39. Column 2 is labeled Total cost (in dollars) with entries 5, 10, 15.
Cost of Ice Cream Cones
A 2-column table with 3 rows. Column 1 is labeled number of ice cream cones with entries 5, 10, 15. Column 2 is labeled Total cost (in dollars) with entries 13, 26, 39.
Cost of Ice Cream Cones
On a coordinate plane, the x-axis is labeled number of ice cream cones and the y-axis is labeled total cost (in dollars). A line goes through points (0, 0) and (5, 13).
Cost of Ice Cream Cones
On a coordinate plane, the x-axis is labeled number of ice cream cones and the y-axis is labeled total cost (in dollars). A line goes through points (3, 1) and (18, 7).
Answer:The answer is B,E and F
Step-by-step explanation:
I'm not sure how to explain but divided 10.40 by 4 and the answer is 2.6 and after that you can figure the rest out. Hope this helps!
Sadie is making punch for her soccer team picnic. She uses 8 quarts of lemon lime soda, 4 pints of vanilla ice cream and 8 cups of orange juice. How many gallons of punch will she have.
Answer:
[tex]3\text{ gallons}[/tex]
Step-by-step explanation:
GIVEN: Sadie is making punch for her soccer team picnic. She uses [tex]8[/tex] quarts of lemon lime soda, [tex]4[/tex] pints of vanilla ice cream and [tex]8[/tex] cups of orange juice.
TO FIND: How many gallons of punch will she have.
SOLUTION:
Amount of lemon lime soda punch [tex]=8\text{ quarts}[/tex]
Amount of vanilla ice cream punch [tex]=4\text{ pints}[/tex]
Amount of orange juice punch [tex]=8\text{ cups}[/tex]
Now,
[tex]1\text{ gallon}=4\text{ quarts}[/tex]
total lemon lime soda punch [tex]=2\text{ gallon}[/tex]
[tex]1\text{ gallon}=8\text{ pint}[/tex]
total vanilla ice cream punch [tex]=0.5 \text{gallon}[/tex]
[tex]1\text{ gallon}=15.77\text{ cups}[/tex]
total orange juice punch [tex]=0.51\text{ gallon}[/tex]
Hence total gallon of punch [tex]=2+0.5+0.51[/tex]
[tex]\approx3\text{ gallon}[/tex]
Hence sadie has total [tex]3\text{ gallons}[/tex] of punches
PLEASE HELP
Circle A has circumference 2 2/3 m. Circle B has a diameter that is 1 1/2 times as long as Circle A’s diameter. What is the circumference of Circle B?
The circumference of Circle B is 4 meters.
Convert mixed number to fraction:
Circumference of Circle A = 2 2/3 m = 8/3 m
Find the diameter of Circle A:
Circumference = π * diameter
8/3 m = π * diameter_A
diameter_A = 8/3π m
Find the diameter of Circle B:
diameter_B = 1 1/2 * diameter_A = 3/2 * (8/3π) m
diameter_B = 4 / π m
Find the circumference of Circle B:
Circumference = π * diameter_B
Circumference of Circle B = π * (4 / π) m
Circumference of Circle B = 4 m
Therefore, the circumference of Circle B is 4 meters.
c3 if c = 2 need help
Answer:
6
Step-by-step explanation:
If c is 2 then that means you would multiply 2 and 3 to get 6
what 1/6 divided by 5
Answer:
1/30
Step-by-step explanation:
Answer:
1.2
Step-by-step explanation:
(simplified)
Jackson purchases a new car for 48,000 The cars value is modlee by the expression 48000(0.76)^t where y represents the cars value and t represents time in years what is the decay rate expressed at a percentage
Answer:
i think 48,000
Step-by-step explanation:
Answer:
me to
Step-by-step explanation:
Solve the system of equations.
y = 1/2x + 3
x + y = 6
Question: here is a spinner with 6 pink shaded areas and 6 white shaded areas. If you spin the spinner ONCE, What is the probability (P) your spinner will land on a pink shaded area?
—-I NEED HELP ASAP!!
Answer: 6/12
Step-by-step explanation:
You have a 50% percent chance of landing on the shaded area
What is the volume of this cylinder if its circumference is 125.7 feet
(the height is 80 ft) use 3.14 for pi
A) 100,681.06
B) 100,053.1
C) 10048
D) 32,032
To find the volume of a cylinder given its circumference and height, divide the given circumference by 2π to find the radius then use the formula for the volume of a cylinder πr²h. In this case, the volume of the cylinder is approximately 100,530.4 cubic feet.
Explanation:The volume of a cylinder can be calculated using the formula V = πr²h where V is the volume, r is the radius of the base, h is the height, and π is a constant that is approximately 3.14. Firstly, we need to find the radius. The circumference of the circle, which is the base of the cylinder, is given by the formula C = 2πr where C is the circumference and r is the radius. Given the circumference as 125.7 feet, we can calculate the radius (r) by dividing the circumference by 2π. Therefore, r = 125.7/(2*3.14) = 20 feet. Once we have the radius, we can calculate the volume of the cylinder using the formula V = πr²h. Substituting r = 20 feet and h = 80 feet, we get V = 3.14 * (20)^2 * 80 which equals 100,530.4 cubic feet. Hence, the closest answer would be option (B) 100,053.1.
Learn more about Volume of a Cylinder here:https://brainly.com/question/16788902
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Simplify (32)2
A) 9
B) 18
C) 27
D) 81
Answer:
D)81
Step-by-step explanation:
Mrs. Barto has a pet rabbit and wants to build a pen for it. She has 3 pieces of lumber: one is 3 ft, one is 7 ft, and the other is 8 ft long. Can she build a closed triangular pen with these three boards (will the boards form a triangle)?
Answer:
Yes, it is possible
Step-by-step explanation:
In a triangle, the length of the longest side of the triangle cannot be larger than the sum of the lenghts of the two shortest sides.
In formula, this means that:
[tex]c\leq a+b[/tex]
where
c is the length of the longest side
a, b are the lengths of the shortest side
In this problem, we want to build a triangle using 3 pieces of lumber, each of length:
a = 3 ft
b = 7 ft
c = 8 ft
We can verify that the length of the longest piece of lumber is less than the sum of the lengths of the other two sides, so:
[tex]8\leq 3+7 = 10[/tex]
Therefore, yes, it is possible to build a closed triangular pen.
The question is about the Triangle Inequality Theorem in Geometry. It asks if a triangle can be formed with given lengths of 3 ft, 7 ft, and 8 ft. By verifying with the theorem, we can confirm that a triangle can be formed.
Explanation:The subject of the question is determining if a triangle can be formed with three given lengths. This topic belongs to Geometry, a branch of Mathematics. To form a triangle, the lengths must satisfy the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side. In this case, we can plug our given lengths into this theorem:
3 ft + 7 ft > 8 ft3 ft + 8 ft > 7 ft7 ft + 8 ft > 3 ftAll these inequalities hold true, so yes, Mrs. Barto can build a closed triangular pen for her pet rabbit with the three pieces of lumber.
Learn more about Triangle Inequality Theorem here:https://brainly.com/question/1163433
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help me find
2/9 + something = 1
Answer:
7/9
Step-by-step explanation:
There are 9/9 in one whole, so if we have 2/9 now, we need another 7/9 to make 9/9: 2/9 + 7/9 = 9/9 = 1
Answer:
7/9
Step-by-step explanation:
1-2/9=7/9
Un grupo de turistas gasta $ 153 para alquilar tubos y aletas. Se alquilan un total de 12 snorkels y 15 pares de aletas. Alquilar un snorkel cuesta tres veces más que alquilar un par de aletas. ¿Cuánto cuesta alquilar un snorkel? Cuesta $ alquilar un snorkel.
Answer:
The cost to rent a snorkel is 9$
(espanol) el costo de un snorkel es de 9$
Step-by-step explanation:
(English)Given that the group of tourists have spent $153 in renting snorkels and fins and there are 12 snorkels and 15 pairs of fins being rented, allow x to be the amount paid for the rent of the snorkels and y to be the rent for pairs of fins then 12x + 15y = 153. Given also that the rent for a snorkel is three times the rent of a pair of fins then x = 3y then, 12(3y) + 15y = 153. Simplify the equation, 36y + 15y = 153. 51y = 153. Solve for y by dividing both sides of the equation by 51 then, y = 153/51 = 3. Therefore, renting a pair of fins costs $3. To compute for the rent of a snorkel, use the equation x = 3y then, x = 3($3) = $9.
(Espanol) Dado que el grupo de turistas han gastado $153 en el alquiler de snorkels y aletas y hay 12 snorkels y 15 pares de aletas que se alquilan, permitir x para ser la cantidad pagada por el alquiler de los snorkels y y para ser el alquiler para pares de aletas entonces 12x + 15y 153. Dado también que el alquiler para un snorkel es tres veces el alquiler de un par de aletas y luego x a 3y, entonces, 12 (3y) + 15y a 153. Simplifique la ecuación, 36y + 15y a 153. 51y a 153. Resuelva para y dividiendo ambos lados de la ecuación por 51 entonces, y á 153/51 a 3. Por lo tanto, alquilar un par de aletas cuesta $3. Para calcular el alquiler de un snorkel, utilice la ecuación x á 3y, a continuación, x a 3($3) a $9.
Jake made these miniature golf scores: 2, 3, 2, 4, 3, 3, 3, 4, 2, 3, 4, 2, 4, 4, 9, 3, 4, 4.
Match the measure to the corresponding value for these scores.
mode
median
range
mean
7
3.5
4
3
Answer:
Mode is 4 median is 3 range 7 mean 3.5
Step-by-step explanation:
Please help me I understand everything else but I don’t know what to do
A farmer has 45 acres of land and plants 17 apple trees on each acre. How many trees in total did the farmer plant?
765 trees
775 trees
865 trees
875 trees
Answer:
765
Step-by-step explanation:
17 * 45 = 765
Answer:
765
Step-by-step explanation:
1. Approximate the length of the hypotenuse to
the nearest tenth using a calculator.
Answer:
What is the answer?
Step-by-step explanation:
Hector puts a principal of $5,600 in a savings account with a simple interest rate of 8%. After several years, he
withdraws the balance of $11,424. How many years did he leave his investment in this particular savings account?
Simple interest: I = Pirit
11 years
12 years
13 years
14 years
Done
Answer:
13 years
first calculate interest and use formula
SI=ptr/100.
Answer:
13
Step-by-step explanation:
Consider the system of equations below. What could be the first step in solving the
system of equations using elimination?
2x + 3y = 8
2x + 6y = 12
Add the two equations.
Add 4 to both sides of the first equation.
Multiply the first equation by -1
Multiply the second equation by 2.
Answer:
(A) Add the two equations.
Step-by-step explanation:
Solved by addition/elimination method.
Let me know if I'm wrong.
<3
If the vertex of a parabola is (8,10) , what is the axis of symmetry?
Answer:
x = 8
Step-by-step explanation:
The axis of symmetry for graph is always set up as "x="
So, if the x in this ordered pair is 8, then the axis of symmetry is also 8.
(I have posted a picture below as proof...)
help ASAP pls :) brainly to whoever has the right answer first :D
Answer:
0.02 (rational)
2 (rational)
Square root of 2 (irrational)
Square root 1/2 (irrational)
Step-by-step explanation:
Rational numbers are numbers that can be in form of a/b such that a and b are not zeros. In other words, a and b are integers ranging from 1 to infinity.
Conversely, irrational numbers are numbers that are endless and are non repeating digits after decimal point.
Thus, from the questions above;
[tex]0.02 = \frac{2}{100} = rational \: number[/tex]
[tex]2 = \frac{2}{1} = rational \: number[/tex]
[tex] \sqrt{2} = 1.41421356 = irrational \: number[/tex]
[tex] \sqrt{ \frac{1}{2} } = 0.70710678 = irrational \: number[/tex]
Ever since he broke his wrist last summer, Carlos never skateboards without his safety equipment. In the Reply box below, copy and paste these headers to identify your answers: 1. Risk the person is taking or the steps he or she is taking to avoid a risk: 2. Reason why:
Answer:
Carlos is risking breaking another bone or getting hurt because he doesn't use any safety equipment to prevent it from happening.
Step-by-step explanation: