Answer:
radius = 6 cm
Step-by-step explanation:
The volume (V) of a sphere is calculated as
V = [tex]\frac{4}{3}[/tex] πr³ ← r is the radius
Given V = 288π, then
[tex]\frac{4}{3}[/tex] πr³ = 288π
Multiply both sides by 3 to clear the fraction
4πr³ = 864π ( divide both sides by 4π )
r³ = 216 ( take the cube root of both sides )
r = [tex]\sqrt[3]{216}[/tex] = 6
Thus the radius of the sphere is 6 cm
To find the sphere's radius from its given volume of 288pi cm^3, we use the volume formula V = (4/3) π r³ and solve for r, resulting in a radius of 6 cm.
Explanation:The student is asking for the radius of a sphere given its volume, which is 288pi cm³. To find the radius, we need to use the formula for the volume of a sphere:
V = (4/3) π r³
Where V is the volume and r is the radius. We can solve for r by rearranging the formula:
r = √[3V / (4π)]
In this case, substituting the given volume into the equation:
r = √[3(288π) / (4π)]
r = √[864π / (4π)]
r = √[216]
The radius of the sphere is 6 cm.
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Natalia Leon bought a new bicycle for $248. The sales tax rate is 6 percent. What is the total purchase price
a. $368.22
C. $262.88
b. $234.66
d. $12.40
Answer:
c. $262.88
Step-by-step explanation:
248× 0.06= $14.88
248+14.88= 262.88
Select the three equations that pass through the points (-4, -16) and (5,2).
y + 4 = 2(x - 16)
y-2 = 2(x - 5)
y=2x-8
y + 16 = 2(x + 4)
DONE
Answer:
It's B,C,D
Step-by-step explanation:
Answer:
its b,c, and d
Step-by-step explanation:
The equation can be used to find the measure of angle LKJ. Triangle L K J is shown. Angle J L K is a right angle. The length of L K is 7.7 centimeters and the length of L J is 8.9 centimeters. Angle L K J is x. What is the measure of angle LKJ? Round to the nearest whole degree. 41° 45° 49° 55°
Answer:
C, 49°.
Step-by-step explanation:
Cause i said so
Answer:
C, 49.
Step-by-step explanation:
The second side of a triangular deck is 4 feet longer than the shortest side , and the third side is 4 feet shorter than twice the length of the shortest side. If the perimeter of the desk is 76 feet , what are lengths of the three sides
The lengths of the three sides of the triangular deck are 19 feet, 23 feet, and 34 feet. The shortest side is 19 feet, the second side is 23 feet, and the third side is 34 feet, and they add up to a perimeter of 76 feet.
Let's denote the length of the shortest side of the triangular deck as "x" feet.According to the problem:The second side is 4 feet longer than the shortest side, so its length is "x + 4" feet.The third side is 4 feet shorter than twice the length of the shortest side, so its length is "2x - 4" feet.Now, we can use the perimeter formula for a triangle, which is:Perimeter = Sum of all sidesIn this case, the perimeter is given as 76 feet, so we can write:x + (x + 4) + (2x - 4) = 76Now, let's solve for x:Combine like terms:4x = 76Divide both sides by 4:x = 19So, the shortest side of the triangular deck is 19 feet.Now, we can find the lengths of the other two sides:The second side is "x + 4," which is 19 + 4 = 23 feet.The third side is "2x - 4," which is 2 * 19 - 4 = 38 - 4 = 34 feet.Therefore, the lengths of the three sides of the triangular deck are 19 feet, 23 feet, and 34 feet.For more questions on sides -
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(- 7 10 ÷ - 2 5 ) × (6 − 1.25) =
Answer: 134.9
Step-by-step explanation: Simplify the expression.
Hope this helps you out!
What is the answer for 4/8-2/5
Answer:
4/8 - 2/5 = 1/10
How do you isolate the variable in 3x=9
Answer:
x = 3
Step-by-step explanation:
you would divide both sides by three to get the x alone giving you
x = 9/3
Which function has a range of y < 3?
y=3(2)*
y=2(3)
y=-(2)*+ 3
O y=(2]*_3
Answer:
The function given by [tex]y = - (2)^{x} + 3[/tex] will have a range of y < 3.
Step-by-step explanation:
The function given by [tex]y = - (2)^{x} + 3[/tex] will have a range of y < 3.
This is because, for any real values of x, the term [tex]- (2)^{x}[/tex] will have a negative value. If we put x = 1, then, [tex]- (2)^{x}[/tex] = - 2, and for x = -1, then [tex]- (2)^{x}[/tex] = - 0.5.
That means [tex]- (2)^{x} < 0[/tex] for all real x.
Hence, [tex]- (2)^{x} + 3[/tex] < 0 + 3
⇒ y < 3 for all real x. (Answer)
Find the measure of x in each figure
Answer:
The answer is in both because, the x goes into 3 accordingly. Also in 30 degrees you move upward, and they both factor into the same equations.
Answer:
Step-by-step explanation:
2x2 what is the answer to this math problem
Answer: The answer is 4.
Explanation: It is 4 because if you add 2 plus 2 you will get 4. Or if you put 2 sets of 2 it also equals 4.
The height of a tree in feet, y, is modeled by the equation y = 2.5x + 3, where x represents
the age of the tree in years. How old will the tree be when it is 33 feet tall?
Answer:
85.5 feet tall
Step-by-step explanation:
2.5(33)+3
82.5+3
85.5
Please help!!!!!!!!!!!!
Answer:
The fraction is: [tex]$ \frac{\textbf{21}}{\textbf{110}} $[/tex]
Step-by-step explanation:
Given that the income is 66000 $ and the amount spent on taxes is 12600 $.
Therefore, the ratio of the amount of taxes and the income
[tex]$ = \frac{12600}{66000} $[/tex]
[tex]$ = \frac{126}{660} $[/tex]
Simplifying, we get: [tex]$ \frac{\textbf{21}}{\textbf{110}} $[/tex]
Hence, the answer.
PLEASE HELP PLEASE
A group of 20 people from the retirement community is visiting the fair today. Each person is between 75 and 79 years old and will participate in either the Pie Eating Contest or the Chili Cookoff. If all 20 people joined the same event, how would the shape of the histogram change compared to the original?
Histogram with title Pie Eating Contest, horizontal axis labeled Age Group (year) with bins 0 to 19, 20 to 39, 40 to 59, and 60 to 79 and vertical axis labeled Number of People with values from 0 to 60 at intervals of 10. The first bin goes to 20, the second goes to 40, the third goes to 60, and the last goes to 50. Histogram with title Chili Cookoff, horizontal axis labeled Age Group (year) with bins 0 to 19, 20 to 39, 40 to 59, and 60 to 79 and vertical axis labeled Number of People with values from 0 to 60 at intervals of 10. The first bin goes to 30, the second goes to 50, the third goes to 40, and the last goes to 10.
The Chili Cookoff would be more skewed.
The Pie Eating Contest would be more skewed.
The Chili Cookoff would be less symmetrical.
The Pie Eating Contest would be more symmetrical.
Answer:
The Pie Eating Contest would be more skewed.
Step-by-step explanation:
In order to answer this, first we need to draw original histograms for both of these two events. Since all of the 20 people from the retirement community is attending one of the events, but we don't know which one, we need to draw new histograms for each of the events (see the attachment).
The only distinction of new histograms is the change in the fourth bin representing the 60-79 age group, since all visitors from retirement community fall into this age group.
A histogram is symmetrical if, when split in half by a vertical line, its left and right half act approximately as an object and its reflection in the mirror.
A histogram is skewed if, when split in half by a vertical line, one of its halves shows much greater values then the other.
So looking at our histograms, if all 20 people went to a Pie Eating Contest, that histogram would become more skewed and if all 20 people went to a Chili Cookoff, that histogram would become more symmetrical, which makes b) the correct answer.
Based on the information given, the correct option is B. The Pie Eating Contest would be more skewed.
From the information given, it was stated that a group of 20 people from the retirement community is visiting the fair today and that each person is between 75 and 79 years old and will participate in either the Pie Eating Contest or the Chili Cookoff.In a situation where all the 20 people joined the same event, the shape of the histogram will change compared to the original as the pie-eating contest would be more skewed.This implies that when split in half by a vertical line, one of its halves will have greater values than the other.
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6. Persevere Mr. Alton wants to be
tickets for a show. The tickets are for
seats in 3 rows with 3 seats in each
row. The total cost of the tickets
is $81. Each ticket costs the same.
What is the cost of one ticket?
Answer:
Each ticket it 9$
Step-by-step explanation:
3 by 3 is 3 times 3
3 times 3 is 9
$81/9 is 9
You are trying to order 1/4 pound of saffron, but the ordering system wants a decimal.What should you type in?
Answer:
Step-by-step explanation:
1/4 = (1 divided by 4) = 0.25
To convert 1/4 pound of saffron to a decimal for an ordering system, divide 1 by 4, resulting in 0.25. Therefore, the appropriate decimal to enter is 0.25.
The question involves converting a fraction to a decimal for the purpose of entering an order quantity in a system. In this case, we want to convert 1/4 pound of saffron into a decimal. To do this, simply divide the numerator (1) by the denominator (4). Therefore, 1 divided by 4 equals 0.25. Hence, you should type 0.25 into the ordering system to order 1/4 pound of saffron.
4 decimals whose sum is 2.35
Answer:
One way you can solve this problem would be to take 2.35/4
2.35/4= .5875
Then you can add .5875 + .5875 +.5875 +.5875
Which equals 2.24
.5875 + .5875 +.5875 +.5875
Hope this helps ;)
To find four decimals whose sum is 2.35, you can set up a system of equations and solve for the values. The four decimals are 0.10, 0.20, 0.15, and 0.15.
Explanation:The question is asking for four decimals whose sum is 2.35. To find these decimals, we can assign variables to each decimal (let's call them a, b, c, and d) and set up an equation: a + b + c + d = 2.35. Since we want the decimals to have only two places after the decimal point, we can express them in hundredths. For example, instead of 0.1, we can write it as 10/100 = 0.10.
Now, we can set up a system of equations:
a + b + c + d = 2.35
a = 10/100
b = 20/100
c = 15/100
d = 15/100
By substituting the values back into the first equation, we have: (10/100) + (20/100) + (15/100) + (15/100) = 2.35. Simplifying the equation, we have 0.10 + 0.20 + 0.15 + 0.15 = 0.60. Therefore, the four decimals whose sum is 2.35 are 0.10, 0.20, 0.15, and 0.15.
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Speed, Time, and Dis
1 a. Noah rides his bike with a constant
speed of 18 km/h. How long will he
take to travel a distance of
54 kilometers?
Answer:
3 hours
Step-by-step explanation:
Recall:
Distance = speed x time
we are given that speed = 18 km/h and distance = 54 km.
hence,
54 = 18 x time (divide both sides by 18 and rearrange)
time = 54/18 = 3 hours
Noah will take 3 hours to travel a distance of 54 kilometers at a constant speed of 18 km/h.
To determine how long Noah will take to travel a distance of 54 kilometers at a constant speed of 18 km/h, we can use the formula for time, which is:
Time = Distance / Speed
Let's calculate Noah's travel time:
Time = 54 km / 18 km/h = 3 hours
Noah will take 3 hours to cover the 54-kilometer distance on his bike.
What is the solution to x2 = 225?
O
A. X = 15 or x =
-15
O B. X = -15
OC. I = 15
D. r = 5 or x = -:
Dan
Answer:
x = ± 15
Step-by-step explanation:
Given
x² = 225 ( take the square root of both sides )
x = ± [tex]\sqrt{225}[/tex] = ± 15
That is x = - 15 0r x = 15
Answer:
Step-by-step explanation:
X² = 225
Finding the square root of both side
√X² = √225
X = 15 or -15
Students played dodgeball and volleyball for 45 min.They played dodgeball for 11 more minuets than volleyball.How long did they play Dodgeball
Answer:
28 minutes
Step-by-step explanation:
d + v = 45
d = v + 11
time to sub
(v + 11) + v = 45
2v + 11 = 45
2v = 45 - 11
2v = 34
v = 34/2
v = 17 minutes.........volleyball
d = v + 11
d = 17 + 11
d = 28 minutes <=== dodge ball
Answer:
28 mins.
Step-by-step explanation:
A technology company produces two types of calculators.
• They must produce at least 10 and not more than 30 graphing calculators per day.
• Each day, the number of graphing calculators cannot exceed twice the number of scientific calculators produced.
• The number of scientific calculators cannot exceed 40 per day.
If x is the number of graphing calculators produced daily and y is the number of scientific calculators produced daily, what are the constraints ?
10 ≤ x ≤ 30, x < 2y, x < 40.
Solution:
Given x is the number of graphing calculators produced daily and
y is the number of scientific calculators produced daily.
Step 1: A company produce atleast 10 and not more than 30 graphing calculators per day.
⇒ 10 ≤ x < 30
Step 2: Each day, the number of graphing calculators cannot exceed twice the number of scientific calculators produced.
⇒ x < 2y
Step 3: The number of scientific calculators cannot exceed 40 per day.
⇒ x < 40
Hence, the constraints are 10 ≤ x ≤ 30, x < 2y, x < 40.
Triangle X Y Z is cut by line segment C D. Line segment C D goes from side X Y to side Y Z. The length of C D is 15, the length of X Z is 18, the length of C Y is 25, and the length of Y D is 20. Lines C D and X Z are parallel. If and CX = 5 units, what is DZ? 2 units 3 units 4 units 5 units
The length of DZ is 4 units ⇒ 3rd answer
Step-by-step explanation:
Triangle X Y Z is cut by line segment C D, where
C lies on side XY and D lies on the side YZThe length of C D is 15The length of X Z is 18The length of C Y is 25The length of Y D is 20C D and X Z are parallelCX = 5 unitsWe need to find the length of DZ
In Δ XYZ
∵ C ∈ XY and D ∈ YZ
∵ CD // XZ
∴ m∠YCD = m∠YXZ ⇒ alternate angles
∴ m∠YDC = m∠YZX ⇒ alternate angles
In Δs YCD and YXZ
∵ m∠YCD = m∠YXZ
∵ m∠YDC = m∠YZX
∵ ∠Y is a common angle
∴ Δ YCD is similar to Δ YXZ by AAA postulate
- There is a constant ratio between their corresponding sides
∴ [tex]\frac{YC}{YX}=\frac{CD}{XZ}=\frac{YD}{YZ}[/tex]
∵ YC = 25 units
∵ CX = 5 units
∵ YX = YC + CX
∴ YX = 25 + 5 = 30 units
∵ YD = 20 units
∵ YZ = YD + DZ
∴ YZ = 20 + DZ
Let us use the ratio of the corresponding side
∵ [tex]\frac{YC}{YX}=\frac{YD}{YZ}[/tex]
∴ [tex]\frac{25}{30}=\frac{20}{20+DZ}[/tex]
- Simplify [tex]\frac{25}{30}[/tex] by dividing up and down by 5
∵ [tex]\frac{25}{30}=\frac{5}{6}[/tex]
∴ [tex]\frac{5}{6}=\frac{20}{20+DZ}[/tex]
- By using cross multiplication
∴ 5(20 + DZ) = 6(20)
∴ 100 + 5 DZ = 120
- Subtract 100 from both sides
∴ 5 DZ = 20
- Divide both sides by 5
∴ DZ = 4 units
The length of DZ is 4 units
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Answer:
on edge the answer is C.
Step-by-step explanation:
bc it is
Does anyone know this?
Answer:
Just a guess but 101
Step-by-step explanation:
90-79=11. 90+11=101
what is 100-100-100-100-100-100-100-100-100-100-100-100
Answer:
-1000
Step-by-step explanation:
(100-100)-(100+100+100+100+100+100+100+100+100+100)=
= 0 - (100+100+100+100+100+100+100+100+100+100)
= -(100 + 100+100+100 + 100+100+100 + 100+100+100)
= -(100×10)
= - 1000
Answer:
-1000
Step-by-step explanation:
What is -5x-10=10 answer
Answer:
-4
Step-by-step explanation:
-5x-10=10
+10 +10
-5x=20
÷-5 ÷-5
×=-4
In a survey of 3300 people who owned a certain type of car, 825 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car?
Answer: 25%
Step-by-step explanation:
Since 825 people said they would buy the car again, it means they were satisfied with the car
Therefore, the percentage of those satisfied with the car is = (825/3300) x 100 = 25%
A population y of coyotes in a national park triples every 20 years. The function y = 15(3)^x
represents the population, where x is the number of 20 year periods.
a. Find and interpret the y-intercept.
b. How many coyotes are in the national park in 40 years?
Answer:
a. y int. = initial amount of coyotes
b. 135 coyotes
Step-by-step explanation:
a. when x = 0, you get y int. = 15 coyotes. This shows that at the very beginning, you had 15 coyotes.
b. 40 years = two 20 year periods. x = 2 after 40 years
y = 15 * (3)^2
y = 135 coyotes
a. y int. = initial amount of coyotes
b. 135 coyotes
The calculation is as follows:a. when x = 0, you get y int. = 15 coyotes.
This represent that at the very beginning, you had 15 coyotes.
b. 40 years = two 20 year periods. x = 2 after 40 years
[tex]y = 15 \times (3)^2[/tex]
y = 135 coyotes
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What is a equal to?
12=2a
Using the balance method, we find a = 15 by isolating the variable a. Substituting a = 15 back into the original equation, we verify the solution.
To solve the equation 12 = 2a - 18 using the balance method, we aim to isolate the variable a on one side of the equation.
Starting with 12 = 2a - 18, we'll first add 18 to both sides to isolate the term with 2a:
[tex]\[12 + 18 = 2a - 18 + 18\]\[30 = 2a\]\\[/tex]
Next, we divide both sides by 2 to solve for a:
[tex]\[\frac{30}{2} = \frac{2a}{2}\]\[15 = a\][/tex]
Now, let's verify the solution by substituting a = 15 back into the original equation:
[tex]\[12 = 2(15) - 18\]\[12 = 30 - 18\]\[12 = 12\][/tex]
Since the left side equals the right side, the solution a = 15 is verified.
Complete Question:
Solve the following equation using balance method and verify 12 = 2a - 18
A recipe calls for 120 mL of milk for each 200 g of flour.Juan is going to use 1 pound of flour. Estimate the number cups of milk Juan should us
Final answer:
To find how much milk Juan should use for 1 pound of flour, convert the flour to grams (454 g), set up a proportion based on the recipe's ratio, solve for the milk in milliliters, and then convert to cups. Juan will need approximately 1.135 cups of milk, or roughly 1 and 1/8 cups.
Explanation:
The question involves calculating how much milk Juan should use in his recipe based on the amount of flour he has. Since the recipe calls for 120 mL of milk for each 200 g of flour, we need to find out the equivalent amount for 1 pound of flour.
First, let's convert 1 pound of flour to grams, knowing that 1 pound is equivalent to approximately 454 grams. The recipe ratio is 120 mL to 200 g of flour, so we set up a proportion:
200 g flour : 120 mL milk = 454 g flour : x mL milk
To solve for x, we use cross multiplication:
(200 g) * (x mL) = (120 mL) * (454 g)
x = (120 mL * 454 g) / (200 g)
x ≈ 272.4 mL
Since there are about 240 mL in 1 cup of milk, we can convert the milliliters to cups:
x ≈ 272.4 mL / 240 mL/cup
x ≈ 1.135 cups of milk
Therefore, Juan should use approximately 1.135 cups of milk for 1 pound of flour. For ease of measuring, Juan can round this to about 1 and 1/8 cups of milk.
What is 4 9/8 as a simplified fraction
Answer:
5 1/8
Step-by-step explanation:
4 9/8 is an improper fraction since the numerator is greater than the denominator. To simplify it, you can find how many total eighths there are. 4*8 = 32, and 32 + 9 = 41. Therefore, there are 41/8. There are 5 eights in 41, with one as a remainder, so 4 9/8 simplifies to 5 1/8.
The value of the mixed number A = 4 9/8 is A = 5 1/8
What are Mixed Numbers?A mixed number is a whole number, and a proper fraction represented together. A mixed number is formed by combining three parts: a whole number, a numerator, and a denominator. The numerator and denominator are part of the proper fraction that makes the mixed number.
Given data ,
Let the mixed number be represented as A
Now , the value of A is
A = 4 9/8 be equation (1)
On simplifying the equation , we get
A = 4 9/8
A = ( 32 + 9 ) / 8
A = 41 / 8
Now , the value of A is an improper fraction , and to convert in into a mixed number , we get
The value of A = 5 1/8
Therefore , the value of A is 5 1/8
Hence , the mixed number is 5 1/8
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joshua has only dimes and pennies in his piggy bank. he has a total of $23.00 in his bank. the amount of pennies is 20 more than 10 times the amount of dimes. how many dimes and pennies are there
There are 1160 pennies and 114 dimes in the piggy bank.
Step-by-step explanation:
Given,
Worth of money = $23.00 = 23*100 = 2300 cents
1 penny = 1 cent
1 dime = 10 cents
Let,
x be the number of pennies
y be the number of cents
According to given statement;
x+10y=2300 Eqn 1
x = 10y+20 Eqn 2
Putting value of x from Eqn 2 in Eqn 1
[tex]10y+20+10y=2300\\20y=2300-20\\20y=2280[/tex]
Dividing both sides by 20
[tex]\frac{20y}{20}=\frac{2280}{20}\\y=114[/tex]
Putting y=144 in Eqn 2
[tex]x=10(114)+20\\x=1140+20\\x=1160[/tex]
There are 1160 pennies and 114 dimes in the piggy bank.
Keywords: linear equation, substitution method
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Final answer:
Joshua has 114 dimes and 1160 pennies in his piggy bank. This was determined by setting up a system of equations based on the values of the coins and the given relationship between the number of dimes and pennies.
Explanation:
The problem presented is a typical algebraic word problem that requires setting up equations based on the given information about dimes and pennies. We are told that the total value of the coins is $23.00 and that the number of pennies is 20 more than 10 times the number of dimes. To solve the problem, we need to use the fact that the value of a dime is 10 pennies, and then set up a system of linear equations to find the number of each type of coin.
Step-by-Step Explanation
Let's denote the number of dimes as d and the number of pennies as p.The value of the dimes is 10d pennies since each dime is worth 10 pennies.The total value of the dimes and pennies is 23 dollars or 2300 pennies (since 1 dollar equals 100 pennies).According to the problem, p = 10d + 20.The equation representing the total value is thus 10d + p = 2300.Substituting p from the first equation into the second gives us: 10d + (10d + 20) = 2300.Simplifying this equation, we get 20d + 20 = 2300.Subtracting 20 from both sides, we get 20d = 2280.Dividing both sides by 20, we find out that d = 114.Substituting d back into the first equation to find p, p = 10(114) + 20 which gives us p = 1160.Thus, Joshua has 114 dimes and 1160 pennies in his piggy bank.