The required algebraic expression is: 9n - (6n +1)
What is an algebraic expression and how is it formed?
Variables and constants are used to create algebraic expressions using a variety of techniques. It is a mathematical expression made up of terms and includes variables, constants, and algebraic operations like addition, subtraction, etc. When operations like addition, subtraction, multiplication, division, etc. are performed on any variable, the resulting equations are called algebraic expressions. An algebraic expression (or variable expression) is a grouping of terms that have undergone operations like addition, subtraction, multiplication, division, etc.
Let the given number be = n
Therefore, nine times the number = 9n
Also, six times the number = 6n
Again, one more than six times the number = 6n + 1
Given, difference between nine times a number and one more than six times the number.
Using all of the expressions derived above, we curate the algebraic expression as:
Algebraic expression: 9n - (6n +1)
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State the order and type of each transformation of the graph of the function f(X)=4(X+9)^2 as compared to the graph of the base function
Using translation concepts, the function f(x) was evaluated by comparing to the graph of a base function g(x) = x².
stretched vertically by a factor of fourShifted 9 units to the left.What exactly is a translation?In mathematics, a translation is the movement of a shape to the left or right and/or down or up. The translated shapes appear to be the same size as that of the original shape, and thus the shapes are congruent. They were simply shifted in one or even more directions. There's no change in shape because it is simply moved from one location to another.A translation is signified by a change with in function graph, based on operations in its definition including such multiplication or sum/subtraction.
The base function g(x) = x² in this problem was.Multiplied by 4, such that, stretched vertically by a factor of four.Shifted 9 units to the left.Thus, the resultant function is obtained as (X)=4(X+9)²
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Cooper, Sha'NiyaThe sum of three consecutive integers is 177. What is the largest of the integers, and why?
We can represent the sum of the three consecutive integers as:
[tex]n+(n+1)+(n+2)=177[/tex]Then, we need to solve the equation for n, then:
[tex]3n+3=177_{}\Rightarrow3n=177-3\Rightarrow3n=174\Rightarrow n=\frac{174}{3}\Rightarrow n=58[/tex]Then, the largest of the integers is n + 2 or 58 +2 = 60.
The reason is that the other integers are 58, 58 + 1 = 59, that is, 58 and 59.
We can check that:
58 + 59 + 60 = 177.
Last month, Carl earned $4900 after working 152 hours. What does Brian make hourly? [Round your answer to the nearest cent.
We have the following:
To know the amount earned per hour, we must divide the total value of money by the total number of hours worked, like this
[tex]\frac{4900}{152}=32.24[/tex]Which means that per hour Carl earns $ 32.24
Bud Graham owns property in Salinas assessed at $250,000 and pays a property tax rate of $1.96 per $100 of assessed value. He also owns property in Modesto assessedat the same $250,000 and pays property tax at a rate of $21.50 per $1,000 of assessed value. What is Bud's total property tax bill for properties in both towns?$10,275$9,965$11,045$10,996None of these choices are correct.
Ok so first we are gonna calculate the tax bill for each town independently and then we are gonna add their values. The tax rate in Salinas is $1.96 per $100 of assessed value and we know Mr. Graham's property is assessed at $250000 so we can use the rule of three:
$100-----------$1.96
$250000----------x
Where x represents his property tax bill for Salinas. According to the rule of three:
[tex]x=\frac{250000\cdot1.96}{100}=4900[/tex]So he has to pay $4900 in taxes for that property. Now we make the same process for his property on Modesto:
$1000-----------$21.5
$250000----------x
[tex]x=\frac{250000\cdot21.5}{1000}=5375[/tex]So he has to pay $5375 for his property in Modesto. Adding the two bills we know the total property bill: $4900 + $5375 = $10275
A basketball team scored a total of 97 points in a basketball game. They made a total of 42 2-point and 3-point baskets. How many 2-point baskets did they make? How many 3-point baskets did they make? Let the number of 2-point baskets = and the number of 3-point baskets = .
If a basketball team scored a total of 97 points in a basketball game and they made a total of 42 2-point and 3-point baskets. then they made 29 two points basket and 13 three point baskets.
The total points scored by the basketball team = 97 points
Consider the number of 2 points basket they scored as x and number of 3 point basket they scored as y
Then the equation will be
2x+3y = 97
They made a total of 42 2-point and 3-point baskets.
Therefore
x+y = 42
x = 42-y
Use the substitution method on the first equation
Substitute the value of x on the first equation.
2(42-y) +3y = 97
84-2y +3y = 97
y = 97-84
y = 13
Substitute the value of y in the equation
x = 42-y
x = 42-13
x = 29
Hence, If a basketball team scored a total of 97 points in a basketball game and they made a total of 42 2-point and 3-point baskets. then they made 29 two points basket and 13 three point baskets.
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how to find the answer for 15x-9y=-9
The value of "x" in the given linear equation of two variable 15x - 9y = -9 will be x = 0.6(-1+y).
As per the question statement, we are given a linear equation of two variable 15x - 9y = -9 and we are supposed to solve it for the variable "x"
First step would be to isolate "x" from the given equation
15x - 9y = -9
15x = -9 + 9y
15x = 9(-1+y) [Distributive property]
x = 9(-1+y)/15
x = 3(-1+y)/5 [Simplified]
or x = 0.6(-1+y)
Hence, the value of "x" in the given linear equation of two variable 15x - 9y = -9 will be x = 0.6(-1+y).
Linear equation: An equation is said to be linear if the maximum power of all the variable is consistently 1. It is also known as one-degree equation.To learn more about linear equation and similar concepts, click on the link given below:
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Marshall has 3 bottles of water. Together, Marshall and Scott have at most 12 bottles of water. Let x represent the number of bottles Scott may have.
Answer:
If you need to find out how many bottles of water Dave has then at the most it would be 9 bottles
Step-by-step explanation:
Scott has 9 number of bottles.
The total number of bottles is 12
Marshall has 3 bottles of water
let the number of bottles Scott is having is x
using the above data:
3+x=12
x=9
Scott has 9 number of bottles.
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sam is making bread dough. the recipe calls for 4/5 cups of flour and 7/8 teaspoons of salt. if sam wants to use 1 cup of flour how much salt is required to maintain the ratio
The amount of salt that is needed for 1 cup of flour is 1 3/32 cups of salt.
How much salt is needed?Ratio is used to compare two or more variables. It shows the relationship that exists between two or more numbers.
A fraction is a non-integer that is made up of a numerator and a denominator. An example of a fraction is 4/5.
In order to determine the salt that is needed for 1 cup of flour, divide the ratio of salt by the ratio of the cups of flour. Division is the operation that is used in maths to determine the quotient of two or more numbers.
7/8 ÷ 4/5
7/8 x 5/4 = 35 / 32 = 1 3/32 cups of salt
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14. Pick the corner point below that maximizes the following objective function: p=22x+14y (6,5)(0,0)(0,12)(15,0)(11,13)
Okay, here we have this:
Considering the provided function, we are going to replace the coordinate pairs one by one in the function, to observe which of the pairs maximizes the function, so we obtain the following:
(6, 5):
p=22x+14y
p=22(6)+14(5)
p=132+70
p=202
(0,0):
p=22x+14y
p=22(0)+14(0)
p=0+0
p=0
(0, 12):
p=22x+14y
p=22(0)+14(12)
p=0+168
p=168
(15, 0):
p=22x+14y
p=22(15)+14(0)
p=330+0
p=330
(11, 13):
p=22x+14y
p=22(11)+14(13)
p=242+182
p=424
Finally we obtain that the corner point that maximizes the function p=22x+14y is the last option (11, 13).
A dog breeder recorded the weight of a puppy during the first eight months after it was born. The breeder created the equation w = 0.25m + 8.3, where w is the weight of the puppy in pounds and m is the number of months since the puppy was born. What is the meaning of the slope from the breeder's equation?
When the puppy is born, the total weight is 0.25 pounds.
When the puppy is born, the total weight is 8.3 pounds.
For every month after the puppy is born, the weight increases by 8.3 pounds.
For every month after the puppy is born, the weight increases by 0.25 pounds.
Answer:
For every month after the puppy is born, the weight increases by 0.25 pounds.
Step-by-step explanation:
A dog breeder recorded the weight of a puppy during the first eight months after it was born. The breeder created the equation w = 0.25m + 8.3, where w is the weight of the puppy in pounds and m is the number of months since the puppy was born. What is the meaning of the slope from the breeder's equation?
When the puppy is born, the total weight is 0.25 pounds.
When the puppy is born, the total weight is 8.3 pounds.
For every month after the puppy is born, the weight increases by 8.3 pounds.
For every month after the puppy is born, the weight increases by 0.25 pounds.
the equation is: w = 0.25m + 8.3
slope for this = 0.25 so the answer is: For every month after the puppy is born, the weight increases by 0.25 pounds.
Answer:
For every month after the puppy is born, the weight increases by 0.25 pounds.
Step-by-step explanation:
A dog breeder recorded the weight of a puppy during the first eight months after it was born. The breeder created the equation w = 0.25m + 8.3, where w is the weight of the puppy in pounds and m is the number of months since the puppy was born. What is the meaning of the slope from the breeder's equation?
When the puppy is born, the total weight is 0.25 pounds.
When the puppy is born, the total weight is 8.3 pounds.
For every month after the puppy is born, the weight increases by 8.3 pounds.
For every month after the puppy is born, the weight increases by 0.25 pounds.
the equation is: w = 0.25m + 8.3
slope for this = 0.25 so the answer is: For every month after the puppy is born, the weight increases by 0.25 pounds.
My math teacher has the answer as -1/4. I got 1/4 and cannot figure out the negative part.
To find the limit we need to rationalize the function, we achieve this by multiplying by a one written in an appropiate way:
[tex]\begin{gathered} \lim_{h\to0}\frac{2-\sqrt{4+h}}{h}=\lim_{h\to0}\frac{2-\sqrt{4+h}}{h}\cdot\frac{2+\sqrt{4+h}}{2+\sqrt{4+h}} \\ =\lim_{h\to0}\frac{(4-(\sqrt{4+h})^2)}{h(2+\sqrt{4+h})} \\ =\lim_{h\to0}\frac{4-(4+h)}{h(2+\sqrt{4+h})} \\ =\lim_{h\to0}\frac{4-4-h}{h(2+\sqrt{4+h})} \\ =\lim_{h\to0}\frac{-h}{h(2+\sqrt{4+h})} \\ =\lim_{h\to0}\frac{-1}{2+\sqrt{4+h}} \\ =-\frac{1}{2+\sqrt{4+0}} \\ =-\frac{1}{2+\sqrt{4}} \\ =-\frac{1}{2+2} \\ =-\frac{1}{4} \end{gathered}[/tex]Therefore:
[tex]\lim_{h\to0}\frac{2-\sqrt{4+h}}{h}=-\frac{1}{4}[/tex]Dontay has 1 5/8 cups of brown sugar .he needs 1/2 cups of brown sugar to make one batch of cookies. How may batches can dontay make ?
Answer:
3
Step-by-step explanation:
1 5/8 is 13/8, he needs 4/8 so 13/4=3R1 so 3
In a state’s lottery, you can bet $1 by selecting three digits, each between 0 and 9 inclusive. If t he same three numbers Are drawn in the same order, you win and collect $400. How many different selections are possible
There are 1000 different selections possible.
There are 10 digits in total from 0 to 9.
It is required to make a three digit number using 10 digits, where repetition is allowed.
So, in the three digit number, the unit place has 10 possible choices, the tens place also has 10 choices, and the hundreds place has 10 possible choices.
So, the total number of different selections of three- digit numbers can be obtained by multiplying 10 by itself three times.
Total different selection possible = Total different choices to fill the units place ×Total different choices to fill the tens place × Total different choices to fill the hundreds place
Total different selection possible = 10×10×10
= 1000
As a result there are 1000 different selections possible.
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Hi, i need assistance with question 2! need to graph all equations! Precalculus homework!
The graphs of the equations have been obtained.
We are given some equations.
We will find some points for the equations.
And then, we will graph them.
a) y = 2 x + 5
x 0 1
y 5 7
b) 2 x + 3 y = 6
x 0 3
y 2 0
c) y - 4 = 3(x + 2)
y - 4 = 3 x + 6
y = 3 x + 10
x 0 1
y 10 13
d) 4(y - 5) = 2(x + 1)
4 y - 20 = 2 x + 2
4 y = 2 x + 22
x 1 3
y 6 7
e) y = x - 3
x - 2 6
y - 5 3
Therefore, we get that, the graphs of the equations have been obtained.
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The cost (c), in dollars, charged by a car rental agency is calculated using the equation c = 12 +0.29m, where m represents the distancetraveled in miles.Calculate the distance traveled for the cost of $56. 37.
The distance taveled is 153 miles
Explanation:The cost function is given as:
c = 12 + 0.29m
Given cost of $56.37, the distance m is obtained from the following equation:
56.37 = 12 + 0.29m
0.29m = 56.37 - 12
0.29m = 44.37
m = 44.37/0.29
= 153
Relative rates of growth, graphing calculator required. Not that difficult but some rules are needed. Ask me if you have any questions regarding the material. Thanks!
Given:-
[tex]f(x)=\sqrt[]{x},g(x)=\ln (x)[/tex]To find the required option, which is correct.
So we need to find the value when x tends to infinity. so to find the value we substitute infinity in place of x. so we get,
[tex]\begin{gathered} f(x)=\sqrt[]{x} \\ f(\infty)=\sqrt[]{\infty}=\infty \end{gathered}[/tex]Also we get,
[tex]g(x)=\ln (x)=\ln (\infty)=\infty[/tex]So the resulting value is infinity for both.
So the required option is The rate of growth cannot be determined.
which values are solution to the inequality below. Check all applyX^2<64A. 65B. 64C. 7D. -8E> 0F. NO SOLUTION
Answer:
[tex]C\text{ and E.}[/tex]Step-by-step explanation:
[tex]x^2<64[/tex]Take the square root of both sides:
*A positive number has two square roots, one positive, and one negative, which are opposite to each other.
[tex]\begin{gathered} x<\pm\sqrt[]{64} \\ -8Therefore, 0 and 7 are solutions to inequality.Use the sum and difference identities to determine the exact value of the following expression. If the answer is undefined, write DNE.tan17724tan1110241751 + tantan1172424
The Solution:
Given the expression below:
We are required to determine the exact value of the above expression.
Recall:
By Trigonometric identity,
[tex]\frac{\:tan\left(\frac{17\pi\:}{24}\right)-tan\left(\frac{11\pi\:}{24}\right)}{1+\:tan\left(\frac{17\pi\:}{24}\right)tan\left(\frac{11\pi\:}{24}\right)}=\tan (\frac{17\pi}{24}-\frac{11\pi}{24})[/tex]This becomes:
[tex]\tan (\frac{17\pi}{24}-\frac{11\pi}{24})=\tan (\frac{17\pi-11\pi}{24})=\tan (\frac{6\pi}{24})=1[/tex][tex]undefined[/tex]Therefore, the correct answer is 1
The circle below has center A.The lenght of AB is in milliliters
ANSWER
[tex]AB=12\text{ }mm[/tex]EXPLANATION
We want to find the length of AB.
The length of AB represents the radius of the circle since it is the distance from the center of the circle to the circumference.
We are given that the diameter of the circle is 24 mm. The radius of a circle is half of its diameter, hence, the radius of the circle is:
[tex]\begin{gathered} r=\frac{24}{2} \\ r=12\text{ }mm \end{gathered}[/tex]Therefore, the length of AB is:
[tex]AB=12\text{ }mm[/tex]That is the solution.
Divide (41°48') = 4.
The division of 41°48' by 4 gives the result 10°27'.
What is termed as the division?Multiplication is the inverse of division. If 3 groups of 4 add up to 12, 12 divided into 3 equal portions adds up to 4 in each group in division. Each component of a division eqn has its own name.Dividend: A dividend is indeed the number divided during the division process.Divisor: The divisor is the number in which the dividend is divided.Quotient: A quotient is an outcome of the division process.Remainder: We can't always divide things exactly. There could be an extra number. The leftover number is known as the remainder.The following describes the relationship between such four parts:
Dividend = Divisor x Quotient + Remainder
For the given expression,
(41°48') divided by 4.
= 41°48' / 4
= 10°27'.
Thus, the division of the expression 41°48' by 4 gives 10°27'.
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Converting linear function formulas
A linear equation has the conventional form Ax+By=C. A slope-intercept form equation (y=mx+b) must have the x and y on the same side of the equal sign and the constant on the opposite side in order to be converted to standard form. To relocate terms, use inverse operations.
What is a formula for linear form?Linear equations come in three main types:
shape of a point-slope: y - y1 = m (x-x1)
typical form: Ax + By = c
Y = mx + b is the slope-intercept formula.
A linear equation with one variable is written in standard form as ax + b = 0, where a 0 and x is the variable. A linear equation with two variables is written as ax + by + c = 0, where the variables are a 0, b 0, x, and y.
A formula's initial sign is usually an equal sign (=).
To enter a formula, click the desired cell.Click in the formula bar to begin the formula with the function. ... or begin entering the formula into the cell.When the formula's arguments are full, press Enter to display the formula's output in the cell.To Learn more About linear equation, Refer:
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The Wycoffs are planning their next family night. They always have dinner out somewhere and then do something fun together. There are 2 adults and 7 children in the family. Each family member is allowed 3 meal suggestions, and each child is allowed 4 activity suggestions. Assuming no family members choose the same thing, how many different family night possibilities are there?
Answer
756 possible family nights
Step-by-step explanation
There are 9 family members ( = 2 adults + 7 children)
Given that each family member is allowed 3 meal suggestions, then there are 9x3 = 27 meal suggestions.
Given that each child is allowed 4 activity suggestions, then there are 4x7 = 28 activity suggestions.
Each family night consists of 1 meal and 1 activity. Therefore, there are 27x28 = 756 possible family nights
Which of the following could be an algebraic expression for the total cost of dinner, less a $5 coupon, divided by 6 people?
6x − 5
6x(5)
(x − 5) ÷ 6
5 − 6x
Answer:
6x - 5
Step-by-step explanation:
a fruit package company produced peaches last summer whose weights were normally distributed with the mean 14 ounces and standard deviation 0.4 ounce. among a sample of 1000 of those peaches about how many could be expected to have any weights of more than 12.6 ounces?round to the nearest whole number as needed
Let x be the random representing the weights of the peaches produced by the company. Since the weights are normally distributed and the population mean and standard deviation are known, we would apply the formula,
z = (x - mean)/standard deviation
From the information given,
mean = 14
standard deviation = 0.4
For the weights to be more than 12.6 ounce, the equation would be
[tex]z\text{ = }\frac{(12.6\text{ - 14)}}{0.4}[/tex]z = -3.5
Looking at the normal distribution table, the probability corresponding to the z score of - 3.5 is 0.00023
Since we want to determine propability for the weights greater than 12.6 ounce, the required probability would be
1 - 0.00023 = 0.99977
Given that the total number of peaches is 1000, the number of peaches expected to have weights more than 12.6 ounce is
0.99977 * 1000 = 999.77
Rounding to the nearest whole number, it becomes 1000
The number of peaches expected to have weights more than 12.6 ounce is approximately 1000
Describing Supplementary Angle Relationships
► Circle all the problems that show two labeled angles that are supplementary.
Then find the value of x for only the circled problems.
Additional Perspectives. A pair of supplementary angles are two angles whose sum measures 180°. A 110° angle and a 70° angle are two examples of supplementary angles
1) 4x+ 6 = 130
x= 31
2) 9x +36+45 =180
x=11
What is a supplementary angles ?Additional Perspectives. A pair of supplementary angles are two angles whose sum measures 180°. A 110° angle and a 70° angle are two examples of supplementary angles. Consider the following example: Here is a 180° straight line, let's call it Z.If a transversal cuts two parallel lines, the interior angles on the same side of the transversal are supplementary. If a transversal cuts two parallel lines, the exterior angles on the same side of the transversal are supplementary.
1) 4x+ 6 = 130
x= 31
2) 9x +36+45 =180
x=11
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Since the angles are supplementary, their measures add to 180°. In other words: 2x+(2x–2)=180. Solving this equation gives the value of x. In algebra, the letter "x" is frequently used to denote an unknown value. It is referred to as a "variable" or occasionally a "unknown." x is a variable in x + 2 = 7.
What exactly is supplemental angle?Two angles are said to be supplementary if their sums total 180 degrees. A linear pair's two angles, like angles 1 and 2 in the illustration below, are always supplementary. But two angles don't have to be close to one another to be supplementary. Since their measures sum up to 180 degrees, the numbers 3 and 4 in the following figure are supplementary.Complementary angles are two angles with a combined angle of 90 degrees, whereas supplementary angles have a combined angle of 180 degrees. Angles sum right angle, but supplementary and complementary angles don't have to be nearby (sharing a vertex and side, or close to each other).Two angles are said to be supplementary angles because they combine to generate a linear angle when their sum is 180 degrees. When two angles add up to 90 degrees, however, they are said to be complimentary angles and together they make a right angle.To know more about supplemental angle refer to:
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Today, John ran 15 miles in 2 hours and 30 minutes. He wants to represent the relationship between the distance he ran, in miles, and the time, in hours, as proportional in order to examine his times at various distances. Write an equation that John can use to represent a proportional relationship between distance, d , in miles, and time, t , in hours.
Answer:
d = 6t
Step-by-step explanation:
Letting d = distance and t = time in hours
we have d = 15 miles
t = 2 hours 30 min = 2 1/2 hours = 5/2 hours
Average speed = 15 ÷ 5/2
= 15 x 2/5 = 6 mph
So the equation is
d = 6t
HELPPPPP ASAPPPP
What will it cost to carpet a rectangular floor measuring 27 feet by 15 feet if the carpet costs $19.05
per square yard?
...
If the carpet costs $19.05 per square yard, it would cost $857.25 to carpet a rectangular floor that is 27 feet by 15 feet.
How are calculations made per square yard?Multiplying the length by the breadth in feet and dividing by 9 yields the square yards (SQYDS). A square yard has a surface area of 9 square feet.Given: A floor rectangle with dimensions of 15 feet by 27 feet.
We need to determine the cost to carpet the floor if the carpet costs $19.05 per square yard.
Area of rectangular floor = 15 × 27
= 405 square feet
We know that,
1 square yard = 9 square feet
So,
405 square feet = 405/9 = 45 square yards
Cost to carpet 1 square yard = $19.05
Cost to carpet 45 square yards = 19.05 × 45
= $857.25
Therefore, Carpeting a rectangular floor measuring 27 feet by 15 feet costs $857.25 if the carpet costs $19.05 per square yard.
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Using only a compass can you find points in a plane that are the same distance from points A and B
You can locate points on a plane (or more specifically, a line segment) that are equally spaced apart from points A and B using a compass.
How can you use a compass to make a locus of points that are equally spaced between A and B?
Draw a straight line AB=7 cm using a ruler.Draw an arc from A using a compass, and then draw another arc that intersects the first one at the point where it crosses AB.From A to the arc, draw a straight line, then extend it to M.Measure 5 cm with a ruler and write AC on the result.We have the required triangle by joining BC.From point C, draw an arc that cuts over AC and BC. From the point where it cuts across AC and BC, draw an arc that cuts across each other. Finally, draw a line that extends from point C to the junction of the two arcs.The same holds true for A as well as O, the intersection of the two lines.Draw a circle with O as the center. This circle will serve as our incircle. Next, draw a perpendicular from O to AB. This perpendicular will serve as the radius.AN is the set of points in our locus that are equally spaced from the lines AB and AC.We must create an incircle, which is a circle inside of a triangle. We can accomplish this by creating an angle bisector from two sides; the intersection point will serve as the incentre. The center of the required circle.
The location where two points are equally distant from one another is known as the angle bisector.
Therefore,
You can locate points on a plane (or more specifically, a line segment) that are equally spaced apart from points A and B using a compass.
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A sphere has a diameter of 4ft . what is its surface area ?The surface area of the sphere is _ ft 2(Type an exact answer in terms of pie .)
The formula of the surface area of an sphere is
[tex]SA=4\pi r^2[/tex]where r is the radius
the radius is half of the diameter
r=4/2
r=2 ft
we substitute the values
[tex]SA=4\pi(2)^2=4\cdot\pi\cdot4=16\pi ft^2[/tex]the surface area is 16pi ft^2
We roll a pair of dice two times. Find the probability that a total of three is rolled each time.The probability that a total of three is rolled each time is ?
we have that
the favorable outcomes are
1 and 2 2 and 1
total outcomes=6*6=36
P(3 in one roll)=2/36=1/18
P(3 rolled 2 consecutive times)=(1/18)^2=0.0031
