The diameter of a spherical basketball is 10in, what is the volume of the basketball?
Answer:
21
Step-by-step explanation:
hard wok
talent
Kevin is 3 times as old as Daniel, 4 years ago, Kevin was 5 times as old as Daniel. How old is Kevin
By using equations to represent the relationship between Kevin and Daniel's ages, we can determine that Kevin is 24 years old.
Kevin is 3 times as old as Daniel. Let's denote Kevin's age as K and Daniel's age as D. From the information given, we can form two equations:
K = 3D
K - 4 = 5(D - 4)
3D - 4= 5D -20
16 = 2D
D = 8
K = 24
Solving these equations simultaneously gives the age of Kevin, therefore, Kevin is 24 years old.
How many of the first 10,000 positive integers contain the digit pair “43” in that order?
Final answer:
There are 209 numbers among the first 10,000 positive integers that contain the digit pair '43' in that order, when considering the different placements of the digit pair in a four-digit number.
Explanation:
To find out how many of the first 10,000 positive integers contain the digit pair "43" in that order, let's consider the different places this pair can occur. The '43' pair can be in the units and tens place, the tens and hundreds place, or the hundreds and thousands place.
For the units and tens place, we have '43' fixed and two remaining places that can be any digit from 0 to 9, so there are 10 times 10 = 100 possibilities. However, we need to exclude the combination '043' as it is not a four-digit number but rather '43', giving us 100 - 1 = 99 combinations.
For the tens and hundreds place, we again have 10 possibilities for the other two places (thousands and units). We do not need to exclude any numbers here because even '043x' represents a valid four-digit number. Thus, we have 10 imes 10 = 100 combinations.
For the hundreds and thousands place, there are only 10 possibilities for the units place, as '430x' represents a valid four-digit number, which results in 10 combinations.
Adding them up, we have a total of 99 + 100 + 10 = 209 numbers that contain the '43' pair in the first 10,000 positive integers.
Henry is building a fence in his backyard for his new puppy he has 36 ft of fencing and wants to fence in a rectangular area what is one set of whole number dimensions of the fenced-in area
What is the product? Enter your answer as a fraction, in simplified form, in the box. 3/8⋅(−3/6)
The product of the given expression of a fraction is [tex]\frac{-3}{16}[/tex].
Given:
An expression : [tex]\frac{3}{8}.(\frac{-3}{6})[/tex]
To find:
The product of the given expression of fractions in simplified form.
Solution:
[tex]\frac{3}{8}.(\frac{-3}{6})\\\\= \frac{3}{8}\times (\frac{-3}{6})\\\\=\frac{-9}{48}\\\\=\frac{-3}{16}[/tex]
The product of the given expression of a fraction is [tex]\frac{-3}{16}[/tex].
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Which equation is in standard form?
x + 2y = 8
x = -2y + 8
2y = -x + 8
Let f(x)=2(3)^x+1 +4. The graph of f(x) is stretched vertically by a factor of 2 to form the graph of g(x). What is the equation of g(x)?
the equation of g(x) after stretching the graph of f(x) vertically by a factor of 2. Therefore, the equation of g(x) is g(x) = 4(3)^x+1 + 8.
To stretch the graph of (f(x)) vertically by a factor of 2 to form the graph of ( g(x)), we need to multiply the entire function (f(x)) by 2.
Given:
[tex]\[ f(x) = 2(3)^{x+1} + 4 \][/tex]
To stretch the graph vertically by a factor of 2, we multiply the function by 2:
[tex]\[ g(x) = 2 \cdot f(x) \][/tex]
Substitute the expression for [tex]\( f(x) \):[/tex]
[tex]\[ g(x) = 2 \cdot [2(3)^{x+1} + 4] \][/tex]
Now, distribute the 2 inside the brackets:
[tex]\[ g(x) = 4(3)^{x+1} + 8 \][/tex]
This is the equation of [tex]\( g(x) \)[/tex] after stretching the graph of [tex]\( f(x) \)[/tex] vertically by a factor of 2.
Therefore, the equation of [tex]\( g(x) \) is \( g(x) = 4(3)^{x+1} + 8 \).[/tex]
Someone plz tell me if my answers for the two questions are correct.Also help me with question f without telling the answer.
Which equation shows y=34x−52 in standard form? 4x−3y=−10 3x−4y=10 3x−4y=−10 4x−3y=10
Answer: The equation that shows y=(3/4)x-5/2 is standard form is:
Second option: 3x-4y=10
Solution:
y=(3/4)x-5/2
Standard form of the equation Ax+By=C, with A, B, and C integer numbers
The coefficient of "x" and the independent term are fractions. To simplify them, let's multiply both sides of the equation by 4:
4y=4 [ (3/4)x-5/2]
4y=4(3/4)x-4(5/2)
4y=(4/1)(3/4)x-(4/1)(5/2)
4y=[(4*3)/(1*4)]x-(4*5)/(1*2)
4y=(12/4)x-20/2
4y=3x-10
The two variables must be in the same side of the equation and the independent term in the other side, but the coefficient of "x" must be positive, then subtracting 4y and adding 10 both sides of the equation:
4y-4y+10=3x-10-4y+10
10=3x-4y
3x-4y=10
Answer:
its B i took the test explanation:
Can you please help me?
Determine the digits of Y from these clues. The digits of Y add to 16. The first digit is 4 times the third digit. The second digit is 3 times the third digit. Y is a three digit number. 268 826 628 862
Answer: 862
Step-by-step explanation:
Let the third digit of Y be x .
Then , the first digit will be 4x and the second digit will be 3x.
Since , the digits of Y add to 16.
Then we have
[tex]3x+4x+x=16\\\\\Rightarrow\ 8x=16\\\\\Rightarrow\ x=\dfrac{16}{8}=2[/tex]
Thus , the third digit of Y = 2
Then the first of Y digit will be [tex]4(2)=8[/tex]
The second digit of Y will be [tex]3(2)=6[/tex]
Hence, the digits of Y must be 862
What is the value of x?
x = ?
x^2 +6^2 = 10^2
x^2 + 36 =100
x^2 = 64
x = sqrt(64)
x = 8
In a competition where the teams have five members, the rule is that the members of each team must have birthdays in the same months. How many persons are needed in order to guarantee that they can raise a team? But two teams?
To guarantee a team, you would need 13 persons, and to guarantee two teams, you would need 24 persons.
Explanation:The number of persons needed to guarantee that they can raise a team is one more than the number of months in a year. This is because there are 12 months in a year, and to ensure that all team members have birthdays in the same month, you would need at least one person for each month. Therefore, you would need 13 persons to guarantee a team.
To guarantee that there are two teams, you would need a total of 24 persons. This is because each team needs at least one person for each month, and there are 12 months in a year. So, for the first team, you would need 13 persons, and then you would need an additional person for each month to form the second team. This would give you a total of 24 persons to guarantee two teams.
Final answer:
To guarantee that a team can be formed, there needs to be at least one person born in each month of the year. To guarantee that two teams can be formed, you would need at least two people born in each month of the year.
Explanation:
To guarantee that a team can be formed, there needs to be at least one person born in each month of the year. Since there are 12 months, you would need a minimum of 12 people to ensure that a team can be formed.
To guarantee that two teams can be formed, you would need at least two people born in each month of the year, as each team needs five members. So, you would need a minimum of 24 people to ensure that two teams can be formed.
2(b+3c) equivalent expressions
Options:
3(b+2c)
(b+3c) +(b+3c)
None of the above
The correct answer to the given expression 2(b+3c) is 'None of the above' as none of the provided options represent an equivalent expression after the application of distributive property.
Explanation:The expression 2(b+3c) cannot be transformed into any of the given options directly. If we use distributive property, we expand 2(b+3c) to get 2b + 6c, which is equivalent to the original expression.
The options provided, such as 3(b+2c), (b+3c) +(b+3c), or 'None of the above', do not simplify or represent an equivalent expression to 2(b+3c). The correct answer is 'None of the above'. It's important to note that the commutative property of addition, A+B = B+A, and the associative property, (A+B) + C = A +(B+C), suggest that we can regroup or reorder terms in an addition expression without changing its value. However, none of these properties help in finding an equivalent expression among the given options for 2(b+3c).
Please help me Simplify 3x-2x+x-9. I was told my answer was wrong
Amy class went the fair they saw 22 horses and 18 ponies they also saw 18 rabbits and 37 hares compare the the number of horses and ponies to the number of rabbits and hares that the class saw.
Amy's class saw a total of 40 horses and ponies and 55 rabbits and hares at the fair,
The question involves comparing the numbers of two sets of animals seen at the fair: horses and ponies versus rabbits and hares. To solve this, we will first add the number of horses and ponies together and then do the same for rabbits and hares.
Number of horses and ponies combined:
22 horses + 18 ponies = 40
Number of rabbits and hares combined:
18 rabbits + 37 hares = 55
Comparing the two totals:
40 horses and ponies is less than 55 rabbits and hares. Therefore the class saw more rabbits and hares combined than horses and ponies combined at the fair
name a segment skew to Wy
simplify 50 1/2 + 12.3
How do i do 4/7 divided by 1 3/4
make 1 3/4 an improper fraction:
1 3/4 = 7/4
now you have 4/7 divided by 7/4
now reverse the 7/4 and multiply:
4/7 x 4/7 = 16/49
1. A video cassette recorder uses 2m of tape in 3 minutes when set on extended play. The tape is about 240 m long. How many hours can be recorded at this setting?
2. You would burn about 200 calories by walking for 60 minutes. About how many calories would you burn if you walk or 15 minutes?
3. A 17 minute phone call from Boston to Chicago costs $2.38. What is the cost per minute?
Audrey needs to cut 1 meter of yellow ribbon and 28 centimeters of blue ribbon. In total, how many centimeters of ribbon does she need?
centimeters
Answer: She needed 128 cm of ribbon.
Step-by-step explanation:
Since we have given that
Length of yellow ribbon needed to be cut = 1 meter
Length of blue ribbon needed to be cut = 28 cm
We need to find the number of centimeters she needed to be cut.
First of all, we convert meter into centimeter.
As we know that
1 meter = 100 centimeter
So, Total number of centimeters of ribbon she needed is given by
[tex]100+28\\\\=128\ cm[/tex]
Hence, She needed 128 cm of ribbon.
a quiche with a diameter of 12 inches can feed 6 people. can a quiche with a diameter of 10 inches feed 4 people, assuming the same serving size explain your thinking
Final answer:
The area per person served by a 12-inch quiche, it was determined that a 10-inch quiche can indeed feed 4 people with the same serving size, as the area available per person in the 10-inch quiche is sufficient.
Explanation:
To determine whether a quiche with a diameter of 10 inches can feed 4 people at the same serving size as a 12-inch quiche that feeds 6 people, we need to compare the areas of the two quiches. The area of a circle is calculated using the formula A = πr² where A is the area and r is the radius. Since the radius is half of the diameter, the 12-inch quiche has a radius of 6 inches and the 10-inch quiche has a radius of 5 inches.
For the 12-inch quiche:
A12 = π(6²) = 36π
For the 10-inch quiche:
A10 = π(5²) = 25π
So, the 12-inch quiche has an area of 36π square inches and the 10-inch quiche has an area of 25π square inches. To find out if the smaller quiche can serve 4 people, we calculate the area per person for the larger quiche: 36π/6 = 6π square inches per person.
Now, we check to see if the 10-inch quiche provides at least that much area for 4 people: 25π/4 ≈ 6.25π square inches per person. Since 6.25π is greater than 6π, we can conclude the 10-inch quiche can indeed feed 4 people with the same serving size as the 12-inch quiche fed 6 people.
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Kevin tries to climb a wall with a ladder. The length of the ladder is 15 feet and it reaches only 12 feet up the wall. What is the distance between the base of the ladder and the wall?
The solution is Option A.
The distance between the base of the ladder and the wall is 9 feet
What is a Triangle?
A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
Given data ,
Let the triangle be represented as ABC
Now , the height of the wall = 12 feet
The measure of AB = 12 feet
The length of the ladder = 15 feet
The measure of AC = 15 feet
Now , the distance between the base of the ladder and the wall = BC
The measure of BC is given by the Pythagoras Theorem , where
Hypotenuse² = base² + height²
AC² = AB² + BC²
Substituting the values in the equation , we get
15² = 12² + BC²
Subtracting 12² on both sides of the equation , we get
BC² = 15² - 12²
BC² = 225 - 144
BC² = 81
Taking square roots on both sides of the equation , we get
BC = 9 feet
Therefore , the value of BC is 9 feet
Hence , the distance is 9 feet
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The prices of two radios are in the ratio x:y
When the prices are both increased by £20, the ratio becomes 5:2
When the prices are both reduced by £5, the ratio becomes 5:1
Express the ratio x:y in it's lowest terms.
The concept of linear equation and ratios is used to solve for the price of radios. The price of two radios are [tex]x=\pounds 80[/tex] and [tex]y=\pounds 20[/tex].
Given information:
The ratio of prices of two radios is [tex]x:y[/tex].
If the price of both the radios is increased by [tex]\pounds20[/tex], the ratio of price would become 5:2.
The above condition can be written mathematically as,
[tex]\dfrac{x+20}{y+20}=\dfrac{5}{2}\\2x+40=5y+100\\2x-5y=60.........(1)[/tex]
If the prices are both reduced by [tex]\pounds 5[/tex], the ratio will become 5:1.
The above condition can be written mathematically as,
[tex]\dfrac{x-5}{y-5}=\dfrac{5}{1}\\x-5=5y-25\\x-5y=-20\\-x+5y=20.........(2)[/tex]
Add equation (1) and (2), to get the value of [tex]x[/tex] and [tex]y[/tex] as,
[tex]2x-x=60+20\\x=80[/tex]
Solve for [tex]y[/tex] as,
[tex]2x-5y=60\\2\times 80-5y=60\\5y=100\\y=20[/tex]
Therefore, the price of two radios is [tex]x=\pouns 80[/tex] and [tex]y=\pounds 20[/tex].
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If the side of a square is doubled and then increased by 7, the new perimeter is 8 more then 3 times the old perimeter. What is the side of the original square?
To find the side of the original square, we can set up an equation and solve for x.
Explanation:To solve this problem, let's assume that the side length of the original square is 'x'. If we double it, the new side length would be '2x'. Adding 7 to it gives us '2x + 7'.
The new perimeter of the square is 8 more than 3 times the old perimeter, so we can set up the equation: 2(2x + 7) = 3(4x).
Simplifying this equation, we get 4x + 14 = 12x. By rearranging the equation, we find that 8x = 14, which leads to x = 1.75.
Therefore, the side length of the original square is 1.75 units.
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The sum of five consecutive numbers is -75. Which number is the least of these five numbers?
What did the doctor say to the guy who thought he was a wigwam one day and tepee the next?
is the expression 3x + 2x - 4 in simplest form?Explain.
What is the measure of angle x?
Which ordered pairs lie on the graph of the exponential function f(x)=4(5)2xf(x)=4(5)2x ?
Select each correct answer.
(−1,425)(−1,425)
(0,0)
(1,4)
(2,2500)
The ordered pairs lie on the graph of the exponential function [tex]\rm f(x) = 4(5)^{2x}[/tex] is (2,2500) and this can be determined by using the arithmetic operations.
Given :
Exponential Function --- [tex]\rm f(x) = 4(5)^{2x}[/tex]
The following steps can be used in order to determine the ordered pairs lie on the graph of the exponential function:
Step 1 - Write the exponential function.
[tex]\rm f(x) = 4(5)^{2x}[/tex]
Step 2 - Substitute the value of (x = -1425) in the above exponential function.
[tex]\rm f(x) = 4(5)^{2\times -1425}[/tex]
[tex]\rm f(x) = 4(5)^{-2850}[/tex]
By simplifying the above function it does not give the value of f(x) = -1425, therefore, option (A) is incorrect.
Step 3 - Substitute the value of (x = 0) in the above exponential function.
[tex]\rm f(x) = 4(5)^{2\times 0}[/tex]
f(x) = 4
Therefore, option (B) is also incorrect.
Step 4 - Substitute the value of (x = 1) in the above exponential function.
[tex]\rm f(x) = 4(5)^{2\times 1}[/tex]
f(x) = 100
Therefore, option (C) is also incorrect.
Step 5 - Substitute the value of (x = 2) in the above exponential function.
[tex]\rm f(x) = 4(5)^{2\times2}[/tex]
f(x) = 2500
Therefore, option (D) is correct.
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