the diameter is multiple by two of the radius
On the first day, a tourist hiked 9 miles to the east from the camp. On the second day, the tourist hiked a few miles to the north. On the third day, the tourist returned to camp by straight way. If the tourist hiked a total of 90 miles, how many miles did the tourist hike on the third day?
On the third day of the camp miles hiked by the tourist as per given data is equal to 41 miles .
As given in the question,
On the first day,
Miles hiked by tourist is 9 miles to the east from camp.
Let x miles be hiked by tourist on the second day to the north.
let h miles be hiked by tourist on third day
Total distance travelled = 90 miles
It represent the right angled triangle
'h' represents the hypotenuse.
By Pythagoras theorem,
h² = x² + 9² ___(1)
x + h + 9 = 90
h = 81 - x __(2)
Substitute the value h from (2) in (1) we get,
( 81 - x )² = x² + 9²
⇒ 6561 - 162x + x² = x² + 9²
⇒ 162x = 6480
⇒ x = 40
⇒ h = 41 miles
Therefore, on the third day of the camp miles hiked by tourist is equal to 41 miles.
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a word phrase that represents m + 8.
Answer:
see explanation
Step-by-step explanation:
m + 8
can be expressed as
the sum of m and 8
Fins the degree of polynomial 3x^4-0x^3+0x^5
The degree of polynomial 3x^4-0x^3+0x^5 is 4
How to determine the degree of a polynomial?Degree of a polynomial is the highest power that its terms pertain (for multi-variables, the power of term is addition of power of variables in that term).
Therefore, inx^3+3x+5, the degree of the polynomial is 3 as the highest power in its terms is 3. (power and exponent are same thing);
Given in the question;
Polynomial= 3x^4-0x^3+0x^5
The highest degree from observation is of 3x that is equal to 4
Hence, the correct degree will be 4
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What is the remainder when x⁴ x³ 2x² X 1 is divided by x 1?
The remainder is 2 when x⁴ + x³ - 2x² + x + 1 is divided by x - 1.
The given polynomial is x⁴ + x³ - 2x² + x + 1.
The given divisor is x - 1
First we choose a term to multiply with the first term of the divisor such that we get the first term of the polynomial.
(x)(x^3) = x^4
Thus, we multiply the divisor (x - 1) by x^3 which gives x^4 - x^2.
Now we subtract this from the polynomial which gives 2x^3 - 2x^2 + x + 1.
Next we multiply the divisor by 2x^2 which gives 2x^3 - 2x^2. Again we subtract the same from the remaining polynomial 2x^3 - 2x^2 + x + 1 and get x + 1.
Repeating the same we multiply the divisor by 1 which gives x - 1. Subtracting the same from the remaining polynomial x + 1 we get the remainder 2.
Thus, the quotient is x^3 + 2x^2 + 1.
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deb had 2 3/4 pounds of blueberries. deb let her friend clarence eat 1/4 of the blueberries. how many pounds of blueberries did clarence eat?
Deb had 2 3/4 pounds of blueberries. Deb let her friend clarence eat 1/4 of the blueberries. Clarence ate 0.6875 pounds of blueberries.
To find out how many pounds of blueberries Clarence ate, we need to first convert the 2 3/4 pounds to a decimal. We can do this by dividing the numerator (3) by the denominator (4) and adding the result to the whole number (2).
2 3/4 pounds = 2 + (3/4) = 2 + 0.75 = 2.75 pounds
Now we know that Deb had 2.75 pounds of blueberries. To find out how many pounds of blueberries Clarence ate, we need to multiply this amount by the fraction of blueberries he ate (1/4).
2.75 pounds x 1/4 = 0.6875 pounds
So Clarence ate 0.6875 pounds of blueberries.
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in a certain lottery, three numbered balls are randomly drawn from a large basket without replacement. to win, a player's ticket must have each of the numbers drawn in no particular order. the balls are numbered from one to one hundred. if jack buys twenty-one tickets, what is the probability that he will win?
The probability that Jack will win is 0.00015. The result is obtained by dividing the number of tickets that Jack has by the total number of events.
How to calculate the probability?Probability of an event is calculated by dividing the number of favorable outcomes by the total number of events in the sample space.
In a certain lottery are 100 balls numbered from 1 - 100 in a large basket. Three numbered balls are randomly drawn without replacement. To win the lottery, a player's ticket must have each of the numbers drawn in no particular order.
If jack buys 21 tickets, find the probability that he will win!
In any the order, the different triples of tickets that a player can have can be found by a combination.
The total number of events would be
[tex]= \: _{100}C_{3}[/tex]
[tex]= \frac{100!}{3! \:97!} }[/tex]
[tex]= \frac{98 \times 99 \times 100}{2 \times 3}[/tex]
= 161700 different triples
Jack has 21 tickets. So, the probability that Jack will win is
P = 21/161700
P = 0.00013
Hence, Jack will win with the probability of 0.00013.
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Two parallel lines are intersected by a transversal,
forming consecutive interior angles A and B, where
m
What is the value of x?
The value of x is 55 degrees.
What is the supplementary angle?If two lines are parallel and intersected by a transversal, then the consecutive interior angles formed are supplementary, meaning they add up to 180 degrees.
Since we know that m∠A + m∠B = 180 and we know that m∠A = x, we can use this information to find the value of x.
m∠A + m∠B = 180
x + (x+70) = 180
x + x + 70 = 180
2x = 110
x = 55
Therefore, the value of x is 55 degrees.
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When 16 is subtracted from half of the number r, the result is at most 18.
Write this as an inequality and solve to find the possible values of r.
X = 68 is the possible values of r.
How to get the perfect solution?Based on the given conditions,
X÷2-16 18
Rearrange variables to the left side of the
Equation: x/2=18+16
Calculate the sum or difference:
X/2=34
Divide both sides of the equation by the
Coefficient of variable X=34 × 2
Calculate the product or quotient: x=68
An inequality can be represented in four ways: equation notation, set notation, interval notation, and solution graph. Many basic inequalities may be handled by adding, removing, multiplying, or dividing both sides until the variable is all that remains. However, these factors will alter the direction of the inequality: Using a negative number to multiply or divide both sides. Swapping the left and right sides.
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Eight less than five times a number is two less than three times the number into an equation
Please I need this
What is the distance from (- 2 4 to 0 )? Round your answer to the nearest hundredth?
20 units is the required distance between the two given points (-2, 4) and (0, 0).
What is the distance?The measurement of distance is the separation between two objects or points, and it can be quantitative or occasionally qualitative.
In physics, the term "distance" can refer to a physical length or, more commonly, to an estimate based on several other parameters.
The distance between two locations on a plane is the length of the line segment connecting them.
The formula d=((x2 - x1)2 + (y2 - y1)2) is frequently used to determine the separation between two points.
So, we know that the distance formula is as follows:
d=((x2 - x1)2 + (y2 - y1)2)
The given points are: (-2, 4) and (0, 0)
Insert values in the formula to calculate the distance as follows:
d=((x2 - x1)2 + (y2 - y1)2)
d=((0 - (-2))2 + (0 - 4)2)
d= (2)2 + (-4)2
d = 4 + 16
d = 20
Therefore, 20 units is the required distance between the two given points (-2, 4) and (0, 0).
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What are steps in factoring?
The general steps to factor a composite number are dividing the composite number by the smallest prime number, if the division is exact, you have found one of the factors of the composite number.
After that then divide the quotient by the smallest prime number that is greater than the divisor used in step 1. Repeat this step with the quotient until the quotient is a prime number. The prime factors of the composite number are the divisors used in the previous steps and the quotient obtained in step 4.
Factoring is the process of finding the prime factors of a composite number.
For example, if you want to factor the composite number 60, you would begin by dividing 60 by 2. Since 60 is divisible by 2, we know that 2 is a factor of 60. The quotient is 30.
We will then divide 30 by 3 and got 10 as quotient.
Then we divide 10 by 2 and got 5 as quotient. 5 is a prime number, so we know that the prime factors of 60 are 2 x 3 x 5
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Mabel has a 15 year adjustable rate mortgage with a fixed rate for the first 4 years. In the 5th year, the Interest rate rises to 5. 8%. The
remaining balance at the end of the 4th years is $231,975. 40. What is the monthly payment in the 5th year? (4 points)
The monthly payment in the 5th year is $2,005.18
To calculate the monthly payment in the 5th year of the adjustable rate mortgage, you would need to know the remaining balance of the loan at the beginning of the 5th year, the interest rate for the 5th year, and the loan term (number of remaining payments) for the 5th year. With the given information, you can calculate the monthly payment using the following formula:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]
Where:
M = monthly payment
P = remaining balance at the beginning of the 5th year
i = interest rate for the 5th year (expressed as a decimal)
n = loan term for the 5th year (number of remaining payments)
Given that the remaining balance at the end of the 4th year is $231,975.40, and the interest rate for the 5th year is 5.8%
i = 5.8% / 12 = 0.004833
n = (1512) - (412) = 108
M = 231975.40 [ 0.004833(1+ 0.004833)^108] / [(1 + 0.004833)^108 -1]
M = $2,005.18
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Make a mapping diagram for each relation.
{(2, 8), (-1, 5), (0, 8), (-1, 3), (-2, 3)}
Answer: A mapping diagram is a way to visualize a relation by plotting its ordered pairs on a coordinate plane.
For the relation {(2, 8), (-1, 5), (0, 8), (-1, 3), (-2, 3)}, the mapping diagram would look like this:
(x,y)
(-2,3) (-1,3)
(0,8)
(-1,5) (2,8)
In the above diagram, each point represents an ordered pair from the relation. You can see that the relation maps x-coordinates -2, -1, 0, 1 and 2 to y-coordinates 3,3,8,5 and 8 respectively.
Step-by-step explanation:
The difference of c and 6 is greater than or equal to -26
A phrase, "the difference of c and 6 is greater than or equal to -26" as an expression, is c - 6 ≥ -26.
What is an expression?A term is a single mathematical phrase. It might consist of only one variable-a letter-one number-positive or negative-or several variables multiplied but never added or subtracted. A number is placed in front of some nouns that have variables. The number used before a sentence is called a coefficient.
Given:
A phrase: The difference of c and 6 is greater than or equal to -26.
The difference of c and 6 can be expressed as,
c - 6.
And c - 6 is greater than or equal to -26 can be expressed as,
c - 6 ≥ -26.
The expression is c - 6 ≥ -26.
Therefore, the phrase can be expressed as c - 6 ≥ -26.
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Is 3x³ a polynomial?
Yes, 3x^3 is a polynomial. It is a third-degree polynomial, which is a monomial.
A polynomial is a mathematical expression that can be written as the sum or difference of one or more terms, where each term is a constant multiplied by one or more variables raised to a non-negative integer power.
A monomial is a polynomial with only one term. It is of the form ax^n, where a is a constant and n is a non-negative integer. In this case, the constant is 3 and the variable is x raised to the power of 3.
The degree of a polynomial is the highest power of the variable in the polynomial.
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november 16, 2001, was a friday. if each of the years 2004, 2008, and 2012 had 366 days, and the remaining years from 2001 through 2014 had 365 days, what day of the week was november 16, 2014 ?
Sunday is the week was November 16, 2014
We see that there is a 13-year span from November 16, 2001, to November 6, 2014. If each year were 365 days, the total number of days in this 13-year span would be 365 x 13 = 4,745 days.
However, since 3 of the years during this span, each has 1 extra day, the actual number of days in this span is 4,745 + 3 = 4,748 days.
Since 4,748/7 = 678 R2, we know that there were 678 weeks and 2 days from Friday, November 16, 2001, until November 16, 2014. The remainder of 2 tells us that November 16, 2014, was 2 days after Friday, so it was Sunday.
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What is the equation for the parabola?
The equation of parabola is f(x) = y= ax² + bx + c
Here we have to find the equation of the parabola.
In order to find the equation of parabola, here we need to know what is meant by parabola.
The term parabola in math is defined as a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone.
Through the definition, we have found the standard form of parabola equation is expressed as,
=> f(x) = y= ax² + bx + c
Here we have know that the orientation of the parabola graph is determined using the “a” value.
While the value of a is greater than 0 (a>0) then the parabola graph is oriented towards the upward direction.
Whereas the value of a is less than 0 (a<0) then the parabola graph opens downwards.
And the axis of symmetry from the standard form of the parabola equation is given as x= -b/2a.
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What is the perimeter of the following kite?
The perimeter of the following kite is 32.
What do a kite's area and perimeter measure?Perimeter is the total of the sides, whereas area is half the product of the diagonals. Remember that a kite is a quadrilateral with distinct adjacent congruent sides and that a rhombus is a quadrilateral with four congruent sides.
How big is a quadrilateral kite's perimeter?The sides of each pair can be added to determine the kite's perimeter. Kite is another name for a quadrilateral with two sides that are equally long on either side. Therefore, a kite's perimeter is equal to 2(a+b), or twice the length of its two sides.
parameter = 2(a+b)
P = 2[(3+3) + (6+4)]
P = 2(6 + 10)
P = 32.
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Please help thank you
Answer: M=3
Step-by-step explanation: because for every 3 pencils there is 1 student.
jeff will pick a card at random from ten cards numbered 1 through 10. the number on this card will indicate his starting point on the number line shown below. he will then spin the fair spinner shown below (which has three congruent sectors) and follow the instruction indicated by his spin. from this new point he will spin the spinner again and follow the resulting instruction. what is the probability that he ends up at a multiple of 3 on the number line? express your answer as a common fraction.
Answer:
my
Step-by-step explanation:
namajeff
A neighborhood was given a vacant lot in the shape of a rectangle on which to build a park. The neighborhood is considering how to split up the area. Which statements about the formulas for finding areas are true? Check all that apply.
Answer:
area : lxb,..,.................
Answer:
Step-by-step explanation:
These are the statements I think is true:
The parallelogram and rectangle formulas are both the same.
In the trapezoid formula, the bases are added.
Explanation:
I’ll just give you the formulas..
Area for trapezoid:
(a + b) ÷ 2 x h
a & b are the bases, h is for height.
Area for rectangle:
Length x width
Area for parallelogram:
Base x height
(Choose the height that is perpendicular to the base)
Also, I would liek you to know I did not understand the other few choices because ai think they have wrong grammar. But I really tried my best for now.
HOPE THIS HELPS!
Which of the methods is a direct method for solving simultaneous algebraic equations Mcq?
Cramer’s rule is the direct method for solving simultaneous algebraic equations.
Algebraic EquationBecause polynomials are included on both sides of the equal sign, algebraic equations are sometimes referred to as polynomial equations. Variables, coefficients, constants, and algebraic operations like addition, subtraction, multiplication, division, and exponentiation are all components of an algebraic equation.
Cramer’s ruleOne of the key techniques for solving a system of equations is Cramer's rule. In this approach, determinants of matrices are used to compute the values of the system's variables. Cramer's rule is frequently referred to as the determinant technique as a result.
Complete Question is given belowWhich of the methods is a direct method for solving simultaneous algebraic equations?
a) Jacobi’s method
b) Relaxation method
c) Cramer’s rule
d) Gauss seidel method
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At a carnival, you spin a spinner that has four equal-sized sections, each a different color: green, yellow, red, and blue. if you land on green, you win 2 points. if you land on yellow, red, or blue, you lose 1 point. write the expected value equation. e (v) = startfraction 1 over a endfraction (2) startfraction 1 over b endfraction (c) startfraction 1 over d endfraction (e) startfraction 1 over f endfraction (g)
Answer:
a = 4
b = 4
c = -1
d = 4
e = -1
f = 4
g = -1
Step-by-step explanation:
that should be right
Connie deposits $30 into an account. The value of the account, in dollars, can be modeled as V(t) = 30 (1. 05)^t , where t is the time, in years, since opening the account.
To the nearest cent, What is the average rate of change in the value of the account for the first 3 years?
A. $0. 63/year
B. $1. 58/year
C. $3. 15/year
D. $4. 73/year
If Connie deposits $30 into an account. The average rate of change in the value of the account for the first 3 years is: B. $1. 58/year.
How to find the average rate of change?Given data:
Equation V(t) = 30 (1. 05)^t
Where,
t = time, in years, since opening the account = 3 years
Average rate of change = [30 (1. 05)^t] - 30/3
Average rate of change = [30 (1. 05)^5] - 30/3
Average rate of change = ($34.73 - $30)/3
Average rate of change = (#4.73)/3
Average rate of change = $1.58
Therefore the correct option is B.
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suppose a person claims​ that, 2.1​​% of all people in the nation always eat​ out. is this a descriptive or inferential​ statement?
O Descriptive O Inferential
The statement describes the percentage of people in the nation who eat out without making any inferences or assumptions.
The statement made by the person is a descriptive statement. This means that the statement simply describes the percentage of people in the nation who always eat out. It does not make any assumptions or inferences based on the data or evidence given. A descriptive statement is one that simply states facts or information without making any assumptions or interpretations about it. It is important to note that a descriptive statement does not imply any cause and effect relationship between the facts or data given. For example, in this statement, there is no inference being made that the people who eat out are healthier or more likely to be successful than people who don't eat out. It is simply stating the percentage of people in the nation who always eat out.
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Find the length of the third side. If necessary, round to the nearest tenth.
The length of the third side in the right angled triangle is 12 units
What is an equation?An equation shows the relationship between numbers and variables in an expression.
Pythagoras theorem shows the relationship between the sides of a right angled triangle. It is given by:
hypotenuse² = opposite² + adjacent²
From the diagram, let x represent the missing side, hence:
15² = 9² + x²
x² = 144
x = 12 units
The missing side is 12 units
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you drive 60 miles north, then 34 miles west, then 20 miles south. how far are you from where you started?
The minimum distance from the starting point is 52.5 miles
First you travels 60 miles north as shown in the image, then 34 miles west and 20 miles south. We can draw a straight line from the endpoint to the stating point.
We could construct a triangle as shown in the figure. From that we can see that AC is the minimum distance from the start. AC is the hypotenuse of the triangle we have drawn..
To calculate the hypotenuse, we can use the Pythagoras theorem.
Hypotenuse² = base²+alt²
AC² = BC²+ AB²
= 34²+40² = 2756
AC = √2756 = 52.497 = 52.5 miles
So the minimum distance is 52.5 miles.
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Apply the distributive property to factor out the greatest common factor. 27 − 18r =?
The greatest common factor of 27 − 18r = 9(3-2r).
What is the greatest common factor?
In mathematics, the largest positive integer that divides each of the integers is known as the greatest common divisor of two or more integers that are not all equal to zero.
Here, we have
Given: 27 − 18r
We have to determine the greatest common factor by applying the distributive property.
Distributive property = multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together. i.e a × (b + c) = (a × b) + (a × c)
27 − 18r = 9(3-2r)
Hence, the greatest common factor of 27 − 18r = 9(3-2r).
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Is Y =- 3 represent a line parallel to x-axis?
Yes.The equation y = -3 represents a line that is parallel to the x-axis.
In a two-dimensional coordinate system, the x-axis is the horizontal axis and the y-axis is the vertical axis. A line parallel to the x-axis will have a constant y-value, and a line parallel to the y-axis will have a constant x-value.
In this case, the equation y = -3 represents a line that has a constant y-value of -3. This means that for every point on the line, the y-coordinate will be -3 and the x-coordinate can take any value. This line is parallel to the x-axis as it does not change in its x-coordinate, so it does not have a slope and it's equation is a horizontal line.
Note, a line parallel to the x-axis is also called a horizontal line, and a line parallel to the y-axis is also called a vertical line.
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Given the equation 10x−y=15. Find the value of x for which the pair of numbers (x; 3) would be a solution to this equation. Write a complete solution.
The complete solution to this problem is: x = 1.8, y = 3.
What do you mean by equation?Equations can be used to represent relationships between variables and to solve problems. They are written using an equal sign (=) and can include numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.
For example, the equation 2x + 3 = 7 is an equation that states that the expression on the left side (2x + 3) is equal to the expression on the right side (7). The goal is to find the value of the variable x that satisfies the equation. In this case, x = 2 is a solution to the equation.
To find the value of x for which the pair of numbers (x; 3) would be a solution to the equation 10x - y = 15, we need to substitute the value of y with 3 and solve for x. So, we have:
10x - 3 = 15
Next, we can add 3 to both sides to isolate x:
10x = 18
Finally, we can divide both sides by 10 to find x:
x = 1.8
So, for the pair of numbers (x; 3) to be a solution to the equation 10x - y = 15, x must be equal to 1.8.
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