Final answer:
To find the volume of a sphere with a diameter of 6 cm, first determine the radius, which is 3 cm, and then use the formula V = (4/3)πr³ to calculate the volume, resulting in approximately 113.097 cm³.
Explanation:
The volume of a sphere is calculated using the formula V = (4/3)πr³, where V represents the volume and r is the radius of the sphere. When the diameter of the sphere is given as 6 cm, the radius is half of that, which is 3 cm. Therefore, substituting the radius into the formula yields:
V = (4/3)π(3 cm)³ = (4/3)π(27 cm³) = 36π cm³
This results in a volume of approximately 113.097 cm³ (since π is approximately 3.14159).
Find the length of the leg of a 16 90 45 triangle
Lorena has two pieces of ribbons. One piece is 3 meter 14 centimeter long. The other piece is 8 meters 24 centimeters long. How many centimeters of ribbon does Lorena have in all
Side AB is parallel to side DC so the alternate interior angles, angle ABD and angle BDC, are congruent. Side AB is equal to side DC and DB is the side common to triangles ABD and BCD. Therefore, the triangles ABD and CDB are congruent by _______________. By CPCTC, angles DBC and ADB are congruent and sides AD and BC are congruent. Angle DBC and angle ADB form a pair of alternate interior angles. Therefore, AD is congruent and parallel to BC. Quadrilateral ABCD is a parallelogram because its opposite sides are equal and parallel. Which phrase best completes the student's proof?
Final answer:
The triangles ABD and CDB are congruent by the Side-Angle-Side (SAS) postulate, leading to the conclusion that quadrilateral ABCD is a parallelogram.
Explanation:
The triangles ABD and CDB can be proved congruent by the Side-Angle-Side (SAS) postulate. Since side AB is parallel to side DC, the alternate interior angles angle ABD and angle BDC are congruent. With both triangles sharing side DB and having equal sides AB and DC, the two triangles satisfy the conditions of the SAS postulate.
By the Corresponding Parts of Congruent Triangles are Congruent (CPCTC) principle, angles DBC and ADB are congruent as well as sides AD and BC. Since angle DBC and angle ADB form a pair of alternate interior angles, this implies that AD is congruent and parallel to BC. This leads to the conclusion that quadrilateral ABCD is a parallelogram, characterized by its opposite sides being equal and parallel.
Ella surveyed the students at her school to find out if they like math and/or science. The table below shows the results of the survey:
Like Math Do Not Like Math Total
Like Science 41 22 63
Do Not Like Science 7 31 38
Total 48 53 101
If a student likes science, what is the probability that student does not like math?
14.5%
18.4%
34.9%
65.1%
Answer:
34.9
Step-by-step explanation:
A cleaning company charges x dollars per hour to clean floors and y dollars per hour to clean the rest of a house.
-When the company spends 2 hours to clean floors and 3 hours to clean the rest of a house, the total charge is $84.
-When the company spends 1 hour to clean floors and 4 hours to clean the rest of a house, the total charge is $87.
Which ordered pair represents the hourly charges to clean floors and to clean the rest of the house?
A. (12, 20)
B. (15, 18)
C. (18, 15)
D. (20, 12)
Note: Please show work. My teacher checks it.
The hourly charges to clean floors and to clean the rest of the house are $15 and $18, respectively. We determine this by setting up a system of equations from the provided scenarios and solving for x and y.
To solve for the hourly charges to clean floors (x) and to clean the rest of the house (y), we need to set up two equations based on the information provided:
2x + 3y = 84 (from the first scenario)1x + 4y = 87 (from the second scenario)Let's solve this system of equations step by step.
Step 1: From the second equation, we can express x in terms of y:
x = 87 - 4y
Step 2: Substitute this expression for x in the first equation:
2(87 - 4y) + 3y = 84
Which simplifies to:
174 - 8y + 3y = 84
Combining like terms gives us:
-5y = -90
Step 3: Solve for y:
y = 18
Step 4: Now, plug the value of y back into the expression for x:
x = 87 - 4(18)
x = 15
Therefore, the hourly charges to clean floors and to clean the rest of the house are $15 and $18 respectively, which corresponds to option B. (15, 18).
Anthony brings 4 bags of popcorn to a meeting. The bags of popcorn are all the same size. There are 14 people at the meeting. Each person eats the same amount of popcorn, and all of the popcorn is eaten. What fraction of a bag of popcorn did each person eat?
Natalie picked 135 berries in 15 minutes. If she continues picking at that rate, how many total minutes will it take her to pick 486 berries?
Can you please give a step by step explanation? Thank you.
NEED HELP ASAP
Which of the following expressions is equivalent to (-7)(-7)(-7)?
3 · -7
-7 · 3
(-7)3
3-7
According to the order of operations, which of the following operations should be completed first in the following expression?
2(5 - 3)^2 + 6^2
multiply (5 - 3) by 2
square (5 - 3)
simplify (5 - 3)
add (5 - 3) to 6^2
Select all that apply.
Which expressions are equal to "five to the third power"?
5^3
3 · 3 · 3 · 3 · 3
5 · 5 · 5
125
15
243
3^5
The expression -8 · -8 · -8 · -8 can be expressed as _____.
-8^4
(-8)^4
-(8^4)
What is the value of -6^2?
-36
36
-12
12
Find the value of |5| - 4(3^2 - 2).
-11
-33
7
-23
Evaluate 8 ÷ -2 · 4^2 + 9.
-100
-55
73
-23
Simplify -5^2 + 8|-1| + (-3).
30
14
-20
-36
Answer:
The answers are solved below.
Step-by-step explanation:
we have to solve the given expressions
Part A: The expression (-7)(-7)(-7)
[tex] (-7)(-7)(-7)=(-1)^37^3[/tex]
Option 3 is correct
Part B: [tex]2(5 - 3)^2 + 6^2[/tex]
First step to solve the above expression is to simplify (5-3) by BODMAS rule then to square the simplification.
Option 3 is correct.
Part C: To choose the expression "five to the third power"
"five to the third power" is
[tex]5^3=5.5.5=125[/tex]
All 3 represents the expression "five to the third power"
Option 1,3,4 are correct.
Part D: The expression -8 · -8 · -8 · -8
The above expression can be written as
[tex](-8)^4[/tex]
Option 2 is correct
Part E: [tex]\text{The value of } -6^2[/tex]
[tex]-6^2=-(6\times 6)=-36[/tex]
Option 1 is correct
Part F: [tex]\text{The value of } |5| - 4(3^2 - 2)[/tex]
[tex]|5| - 4(3^2 - 2)=5-4(9-2)=5-4(7)=5-28=-23[/tex]
Option 4 is correct.
Part G: Evaluate [tex]\frac{8}{ -2}\times 4^2 + 9[/tex]
[tex]\frac{8}{ -2}\times 4^2 + 9=-4\times 16+9=-64+9=-55{ [/tex]
Option 2 is correct.
Part H: Simplify [tex]-5^2 + 8|-1| + (-3)[/tex]
[tex]-5^2 + 8|-1| + (-3)=-25+8-3=-17-3=-20[/tex]
Option 3 is correct.
2 trifles cost 7 pounds how much does 6 cost
Cost of 6 trifles is 21 pound
Given that;Cost of 2 trifles = 7 pound
Find:Cost of 6 trifles
Computation:Cost of 6 trifles = 6[7 / 2]
Cost of 6 trifles = [3][7]
Cost of 6 trifles = 21 pound
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What is the area of sector GPH? the angle inside the circle measures 80º and the radius from p to h is 15
Answer:
The area of sector GPH is equal to [tex]50\pi\ units^{2}[/tex]
Step-by-step explanation:
we know that
The area of a circle is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=15\ units[/tex]
substitute
[tex]A=\pi(15)^{2}=225 \pi\ units^{2}[/tex]
[tex]360\°[/tex] subtends the complete circle of area [tex]225 \pi\ units^{2}[/tex]
so
By proportion
Find the area of sector GPH
[tex]\frac{225 \pi}{360}\frac{\ units^{2} }{degrees} =\frac{x}{80}\frac{\ units^{2} }{degrees}\\ \\x=80*225\pi /360\\ \\x=50\pi\ units^{2}[/tex]
can someone please help me i got stuck in this question
First 5 multiples of 6: 6, 12, 18, 24, 30 First 5 multiples of 9: 9, 18, 27, 36, 45 What is the least common multiple (LCM) of 6 and 9?
Solution:
We are given the first five multiples of 6 and 9.
First 5 multiples of 6: 6, 12, 18, 24, 30 First 5 multiples of 9: 9, 18, 27, 36, 45If we look carefully, we can see that the smallest number that is common in both multiples is 18.
First 5 multiples of six: 6, 12, 18, 24, 30 First 5 multiples of nine: 9, 18, 27, 36, 45Thus, the LCM of 6 and 9 is 18.
LCM is lowest common multiple
Let's check
2|6,9
3|3,9
3|1,3
LCM=2(3)(3)=18
if LuxRide's revenues in London grow by 20% next year, what will their market share be?
If s = 1 over 2 unit and A = 12s2, what is the value of A, in square units? ____ square unit(s). (Input whole number only.)
Answer:
The value of A is 3 square units.
Step-by-step explanation:
Given: [tex]s=\frac{1}[2}[/tex] unit and A is given by [tex]A=12s^2[/tex]
We have to find the value of A.
Consider the given formula [tex]A=12s^2[/tex]
Put [tex]s=\frac{1}[2}[/tex]
We get,
[tex]A=12(\frac{1}{2})^2[/tex]
Simplify, we have,
[tex]A=12\cdot\frac{1}{4}[/tex]
Further simplify, we have,
[tex]A=3[/tex]
Thus, The value of A is 3 square units.
Could anyone help me with these?
One ounce is about the same as 0.06 pound. What is 0.06 written as a fraction?
Answer:
[tex].06 = \frac{6}{100} = \frac{3}{50} [/tex]
Question 5 of 5 At 7:00 a.m., the temperature was 8°C. What was the temperature at midnight if the temperature was 10° lower? A. −18° C B. −2° C C. 2° C D. 18° C
Can somebody please help me, I’m stumped. Please explain easily to
compare the amount of sand in the top cone of the hourglass to the amount there will be when the height of the sand in the top cone is only one inch.
To compare the amount of sand in the top cone of an hourglass when the height is one inch, calculate the volume using the formula volume = length × width × height. Compare the original volume to the new volume with a height of one inch to determine the difference in the amount of sand.
Explanation:The question asks to compare the amount of sand in the top cone of an hourglass to the amount when the height of the sand in the top cone is only one inch. In an idealized model of the hourglass, the volume of the stack of sand in the top cone can be calculated using the formula volume = length × width × height. From the given information, the volume of the stack is 9 in³. To find the amount of sand when the height is one inch, we can calculate the new volume using the same formula with the new height.
Original volume of stack = length × width × height = 9 in³New volume of stack with a height of one inch = length × width × 1 in.By comparing the original volume of 9 in³ to the new volume with a height of one inch, you can determine the difference in the amount of sand in the top cone of the hourglass.
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The amount of sand in the top cone when the height of the sand is h is h times the amount of sand there will be when the height of the sand is only one inch.
The volume of a cone is given by the formula:
V = (1/3)πr²h
where r is the radius of the base of the cone and h is the height of the cone.
If the height of the sand in the top cone is currently h, then the volume of the sand in the top cone is:
V₁ = (1/3)πr²h
When the height of the sand in the top cone is only one inch, the volume of the sand in the top cone will be:
V₂ = (1/3)πr²(1 inch)
To compare the two volumes, we can divide V₁ by V₂
V₁ / V₂ = (1/3)πr²h / (1/3)πr²(1 inch)
V₁ / V₂ = h / 1 inch
Therefore, the amount of sand in the top cone when the height of the sand is h is h times the amount of sand there will be when the height of the sand is only one inch.
For such more question on height
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what value is most affected by an outlier, the median or the ranhe? explain. can you see these effects in a dot plot
What is 56% written as a ratio?
A pitcher needs more than one pitch to be effective. Dizzy uses his changeup only half as much as his fastball, and to save his arm, he throws a slider a third as much as his fastball. In a 110-pitch game, how many sliders would he throw?
In Dizzy's 110-pitch game, he threw 20 sliders. The answer was found by setting up and solving algebraic equations based on the information given in the question.
Explanation:This question is about using algebra to solve word problems. Let's denote the number of fastballs Dizzy throws as F, the number of changeups as C, and the number of sliders as S.
According to the question, Dizzy throws his changeup half as much as his fastball (C = 0.5F) and his slider a third as much as his fastball (S = F/3). We also know the total number of pitches (110) is the sum of F, C, and S pitches (110 = F + C + S).
We then substitute the expressions for C and S from our first two equations into our third equation to get: 110 = F + 0.5F + F/3. Solving this equation gives us F = 60. We substitute F = 60 into S = F/3 to find that Dizzy threw 20 sliders in the game.
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The opening in a rectangular door frame measures 9 feet by 3 feet. Each of the four doors described in the table measures 9 feet by 3 feet, but have different diagonal lengths. Which door will fit in the rectangular opening?
Door 1: 10 ft
Door 2: 3 square root 10ft
Door 3: 6 square root 2ft
Door 4: 12ft
Answer:B
Step-by-step explanation:
8x+12=10x-8 help me out bruh
A baseball has a diameter of 5.1 inches. Find the volume of the baseball. Round your answer to the nearest tenth. Use 3.14 for pi
Val’s go cart has a gas tank with the dimensions shown below. He uses a gas can that holds 1 gallon of gas, to fill the go cart tank. 1 gallon = 231 inched cubed
A bag contains 8 blue marbles, 6 green marbles, 12 yellow marbles, and 10 orange marbles. A marble is drawn at random from the bag.
What is the probability that the marble drawn will not be blue?
A.) 29
B.) 34
C.) 79
D.) 78
Answer:
C
Step-by-step explanation:
I got it right and here is proof
If it is blurry, just press it and it will be non-blurry
Help me asap please !!
What is the area of 14km and 12km and 8km and 5km and 4km and 9km
Final answer:
Calculate the sum of areas of squares with given side lengths to find the total area.
Explanation:
Area of a Square:
Calculate the area of each square:
14 km x 14 km = (14)² = 196 km²
12 km x 12 km = (12)² = 144 km²
8 km x 8 km = (8)² = 64 km²
5 km x 5 km = (5)² = 25 km²
4 km x 4 km = (4)² = 16 km²
9 km x 9 km = (9)² = 81 km²
Sum of Areas:
Add the areas of all squares together:
196 km² + 144 km² + 64 km² + 25 km² + 16 km² + 81 km² = 526 km²
Therefore, the total area is 526 km².
What is the area of a circle that has a circumference of 48 feet?