Answer:
[tex]Distance\ cover\ by\ Rosa = 141.3\ m[/tex]
Step-by-step explanation:
Given:
Rosa has to skate around a face off circle five times.
[tex]Distance = 5\times circumfrance\ of\ circle[/tex]
Diameter of a circle = 9.0 m
Radius of a circle = [tex]\frac{d}{2} =\frac{9}{2}=4.5\ m[/tex]
Solution:
We know that the circumference of a circle.
[tex]C = 2\pi r[/tex]
Where;
r = Radius of a circle
Substitute [tex]\pi =3.14\ and\ r = 4.5[/tex] in above equation.
[tex]C = 2\times 3.14\times 4.5[/tex]
[tex]C = 28.26\ m[/tex]
So, the circumference of the circle is 28.26 m.
Rosa has to skate around a face off circle five times, so Rosa cover 28.26 m 5 times.
[tex]Distance\ cover\ by\ Rosa = 5\times 28.26[/tex]
[tex]Distance\ cover\ by\ Rosa = 141.3\ m[/tex]
Therefore, the distance cover by Rosa to skate 141.3 m.
Rosa has to skate approximately 141.35 meters to go around the face off circle with a diameter of 9.0m five times.
To calculate how far Rosa has to skate, we need to determine the circumference of the face off circle, which can be calculated using the formula C = pi × d, where C is the circumference and d is the diameter of the circle. Since Rosa skates around the circle five times, we will multiply the circumference by five.
Given that the diameter (d) of the face off circle is 9.0 meters, the circumference is:
C = pi × d = pi × 9.0mC = 28.27m (approximately, using pi = 3.14)Now, we calculate the total distance Rosa skates by going around the circle five times.
Total distance = Circumference × Number of laps
Total distance = 28.27m × 5 = 141.35m
Therefore, Rosa has to skate approximately 141.35 meters around the face off circle.
Suppose you deposit $7500 in a saving account that has as interest rate of 5.5.
If the interest is compounded monthly, what will the approximate balance of this saving account be in 3 years?
Answer:
ok so im going give the equation to fiqure this along with the awnser,
the basic equation is A=P (1+R/N)N(T)
P= Principle (Starting amount)
R= Interest rate
N= Amount of time compounded PER YEAR
T= amount of years
Step-by-step explanation:
so this would be A=$7500 (1+ 0.055/12)12(3)
which come to A=$7500 (1.178948602)
which comes to a total of $8842.11
hope this helps
Final answer:
The balance of a savings account with an initial deposit of $7500 and an annual interest rate of 5.5%, compounded monthly, will be approximately $8863.52 after 3 years.
Explanation:
The question involves the concept of compound interest, more specifically how much the balance of a savings account with an initial deposit of $7500 and an annual interest rate of 5.5%, compounded monthly, will be in 3 years. To calculate this, we use the compound interest formula: A = P(1 + r/n)^(nt), where:
A = the amount of money accumulated after n years, including interest.P = the principal amount (the initial amount of money).r = the annual interest rate (decimal).n = the number of times that interest is compounded per year.t = the time the money is invested for, in years.For the given problem:
P = $7500r = 5.5% or 0.055 (as a decimal)n = 12 (since it's compounded monthly)t = 3 yearsWe can substitute the values into the formula:
A = 7500(1 + 0.055/12)^(12*3)
Calculating this out, we find:
A = 7500(1 + 0.0045833)³⁶
A = 7500(1.0045833)³⁶
A = 7500(1.1811360235)
A = $8863.52 (approximately)
Therefore, the approximate balance of the savings account after 3 years will be $8863.52.
old mcdonald has 100 chickens and goats in the barnyard. Altogether, there are 284 feet. How many chickens and how many goats are in the barnyard?
Answer:
58 chickens, 42 goats
Step-by-step explanation:
there are a total of 100 chickens and goats
c + g = 100....c = 100 - g
there are 284 feet....chickens have 2 feet and goats have 4 feet
2c + 4g = 284
2(100 - g) + 4g = 284
200 - 2g + 4g = 284
-2g + 4g = 284 - 200
2g = 84
g = 84/2
g = 42 <===== goats
c + g = 100
c + 42 = 100
c = 100 - 42
c = 58 <==== chickens
Final answer:
To solve the problem, set up equations based on the number of feet each animal has, then use substitution to find there are 58 chickens and 42 goats in the barnyard.
Explanation:
How to Solve Problems Involving Numbers of Chickens and Goats
Old McDonald has 100 chickens and goats in the barnyard, and altogether, there are 284 feet. To find out how many chickens and how many goats are there, we can set up a system of equations based on the information given. A chicken has 2 feet and a goat has 4 feet. Let's assign the variable C to represent the number of chickens and G to represent the number of goats.
We are given two pieces of information which we will translate into two equations:
Equation 1: C + G = 100 (since there are 100 chickens and goats in total)
Equation 2: 2C + 4G = 284 (since chickens have 2 feet and goats have 4 feet)
To solve for C and G, we can multiply Equation 1 by 2 to align it with the coefficients of Equation 2:
2C + 2G = 200
Now, subtract this new equation from Equation 2 to solve for G:
(2C + 4G) - (2C + 2G) = 284 - 200
2G = 84
G = 42
With G known, we can substitute it back into Equation 1 to find C:
C + 42 = 100
C = 58
Therefore, there are 58 chickens and 42 goats in the barnyard.
The endpoints of cd are C (-4,10) and D (-4,10) the coordinates of the midpoint M of CD are
The endpoints C and D has no midpoint M.
Step-by-step explanation:
step 1: The given endpoints of C and D are (-4,10) and (-4,10)
step 2: Midpoint formula = ((x1+x2)/2 , (y1+y2)/2)
step 3: Here, C(-4,10) = (x1,y1)
D(-4,10) = (x2,y2)
step 4: The midpoint represents the half distance of the line CD. Since C and D are same points, they cannot form a line. Therefore, the endpoints CD have no midpoint.
What is the product (3x-6)(2x2-7x+1)
Answer:
[tex]\large\boxed{6x^3-33x^2+45x-6}[/tex]
Step-by-step explanation:
[tex]\text{Use FOIL:}\ (a+b)(c+d)=ac+ad+bc+bd\\\\(3x-6)(2x^2-7x+1)\\\\=(3x)(2x^2)+(3x)(-7x)+(3x)(1)+(-6)(2x^2)+(-6)(-7x)+(-6)(1)\\\\=6x^3-21x^2+3x-12x^2+42x-6\qquad\text{combine like terms}\\\\=6x^3+(-21x^2-12x^2)+(3x+42x)-6\\\\=6x^3-33x^2+45x-6[/tex]
10 minus three times a number is no more than 61
Answer:
n ≥ -17
Step-by-step explanation:
Writing a symbolic inequality, we get:
10 - 3n ≤ 61
Solve this for 3n by adding 3n to both sides of this equation:
10 ≤ 61 + 3n
Solve for n by subtracting 61 from both sides and then dividing all of the resulting terms by 3:
-51 ≤ 3n (divide both sides by 3):
-17 ≤ n, or
n ≥ -17
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Which statement is correct about the product of 4/5 and 11/9 ?
A. Because 11/9 is greater than 1, the product of 4/5 and 11/9 is greater than 4/5 .
B. Because 11/9 is less than 1, the product of 4/5 and 11/9 is less than 4/5 .
C. Because 11/9 is greater than 1, the product of 4/5 and 11/9 is less than 4/5 .
D. Because 11/9 is less than 1, the product of 4/5 and 11/9 is greater than 4/5 .
Answer:
The answer is A. Because 11/9 is greater than 1, the product of 4/5 and 11/9 is greater than 4/5
9/9 is exactly 1. 11/9 is greater than 9/9, so 11/9 is greater than 1. If I added 4/5, the answer is larger than 11/9, therefore the answer is A.
Answer:
A. Because 11/9 is greater than 1, the product of 4/5 and 11/9 is greater than 4/5
Step-by-step explanation:
Hope this helps!
what is 3y+14-2=0 in substitution
Answer:
y=-4
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
3y+14−2=0
3y+14+(−2)=0
(3y)+(14+(−2))=0 (Combine Like Terms)
3y+12=0
3y+12=0
Step 2: Subtract 12 from both sides.
3y+12−12=0−12
3y=−12
Step 3: Divide both sides by 3.
3y/3= −12/3
y=−4
Answer:
y=−4
What is bigger -8 or 5
5 is bigger because its right of your number line and it isn’t -8 because it below 0 and left of the number
Line V has a slope of 8/9. Line w is perpendicular to V. What is the slope of line W?
Answer:
W = -9/8
Step-by-step explanation:
for two perpendicular lines
W*V = -1
W = 9/8*(-1)
W= -9/8
Final answer:
The slope of line W, which is perpendicular to line V with a slope of 8/9, is -9/8.
Explanation:
The slope of a line perpendicular to another in a two-dimensional plane is the negative reciprocal of the original line’s slope. Given that line V has a slope of 8/9, the slope of the perpendicular line W would be -9/8. This is because the product of the slopes of two perpendicular lines is -1 (negative one). Therefore, the slope of the line W, which is perpendicular to V, is -9/8.
8.4(7x-4)+3.9 simplified
To simplify the expression 8.4(7x-4)+3.9, distribute 8.4 to both terms inside the parentheses and then add 3.9, resulting in 58.8x - 29.7.
Explanation:The problem 8.4(7x-4)+3.9 requires simplification by applying the distributive property and then combining like terms. First, multiply 8.4 by both 7x and -4, and then add the constant 3.9 to the result.
Multiply 8.4 by 7x: 8.4 imes 7x = 58.8x.Multiply 8.4 by -4: 8.4 imes -4 = -33.6.Add the constant: -33.6 + 3.9 = -29.7.Combine the terms: 58.8x - 29.7 is the simplified expression.
Nicole Nichols purchased a new carpet for $287 and a vacuum cleaner for $121. What is the sales tax if she
lives in Iowa where the sales tax rate is 5 percent?
a. $31.99
c. $20.40
b. $19.98
d. $24.48
Answer:
$20.40 is the sales tax if she lives in Ohio where the sales tax rate is 5 percent.
Step-by-step explanation:
-12 * 7/2
Please explain
Answer:-42
Step-by-step explanation:
-12*7/2
Is also represented like this
-12/1*7/2 proper fraction
Multiple -12*7 and divide by 2
-84/2= -42
Answer:
Using BIDMAS the answer equates to -42.
Step-by-step explanation:
A package of 35 pencils cost $5.25. At his rate what is the cost of 1 pencil
Determine the slope of the line that passes through points (0, -4) and (-1,2).
6
-6
-1/6
1/6
Answer:
B) -6
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(2-(-4))/(-1-0)
m=(2+4)/(-1)
m=6/-1
m=-6
the answer is B, -6, because if you graph it the line goes down and it rises up 6
Which of the following is equal to the rational expression when X not equal -4 or 3?
x2 - 4x + 3
X^2+ X - 12
Answer:
A
Step-by-step explanation:
Given
[tex]\frac{x^2-4x+3}{x^2+x-12}[/tex]
Factorise the numerator and denominator
x² - 4x + 3 = (x - 1)(x - 3)
x² + x - 12 = (x + 4)(x - 3), thus
= [tex]\frac{(x-1)(x-3)}{(x+4)(x-3)}[/tex] ← cancel (x - 3) on numerator/denominator
= [tex]\frac{x-1}{x+4}[/tex] → A
Rational expression are written as fractions. The simplified form of the expression is [tex]\frac{x-1}{x+4}[/tex]
Rational expressionsRational expression are written as fractions.
Given the rational expression
[tex]\dfrac{x^2-4x+3}{x^2+x-12}[/tex]
Factorize the numerator and denominator
[tex]=\dfrac{x^2-4x+3}{x^2+x-12}\\=\dfrac{x^2-3x-x+3}{x^2+4x-3x-12}\\=\frac{(x-3)(x-1)}{(x+4(x-3)} \\=\frac{x-1}{x+4}[/tex]
Hence the simplified form of the expression is [tex]\frac{x-1}{x+4}[/tex]
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A line is perpendicular to y= 1/2x-9 and intercepts the point (3,2) what is the perpendicular line
Answer:
Y= -2x +8
Step-by-step explanation:
We know the line is perpendicular so the slope is negative inverse of 1/2, which is -2.
Now to find b, plug into equation
Y= -2x+ b
2= -2(3) +b
2= -6+ b
2+6= b
8=b
Answer:
-2x+8
Step-by-step explanation:
How would you solve 4n-2n=4?
Answer:
n = 2
Explanation:
Simplify both sides of the equation
4n − 2n = 4
4n + −2n = 4
(4n + −2n) = 4 (Combine Like Terms)
2n = 4
2n = 4
Divide both sides by 2
2n / 2 = 4 / 2
n = 2
4n-2n=4
4n-2n= 2n
2n=4
÷2
n=2
p. John roller skates with a constant
speed of 12 miles per hour. How long
will he take to travel a distance of
30 miles?
Answer:
2 1/2 hours
Step-by-step explanation:
1. multiply 12 by 2 to get 24
2. divide 12 by 2 to get 6 mph (miles per hour)
3. Add the 6 and 24
26.35 rounded to the nearest hundred
Answer:
Nearest hundred: 0
Nearest hundredth: 26.35
Step-by-step explanation:
The hundred place value is three numbers to the left of the dot.
The two hundreds that are nearest to 26.35 are 0 and 100. To decide if you should round up (to 100) or round down (to 0), use the place value that is to the right of the hundred place: the number you are using is 2.
The rule for rounding:
Round up if the place value is 5 or more
Round down if the place value is 4 or less
Since 2 is "4 or less", round down to 0.
Since 26.35 is closer to 0 than 100:
26.35 => 0 when rounded to the nearest hundred
In case you meant hundredth:
The nearest hundredth means two decimal places, or two numbers right of the dot.
The number 26.35 already has two decimal places, so rounded to the nearest hundredth is still 26.35.
26.35 => 26.35
Supposed that a defined population is all men and a survey is being conducted. which of these is an example of selection bias?
Answer:no it's not because bias Is your opinion ( like if you say dogs are the best that's your opinion only
Step-by-step explanation:
Answer:
Excluding women with children from the selection process of the survey
Step-by-step explanation:
The correct answer is: Excluding women with children from the selection process of the survey.
systems of equations
15x-4y=62
5x+8y=86
Answer:
y = 7 and x = 6
Step-by-step explanation:
15x-4y=62 ---------------------------(i)
5x+8y=86-----------------------------(ii) X 3
15x+24y=258---------------------------(iii)
(iii)-(i)
28y = 196
y = 7
Sub. for y in (I) to get x
x = 6
Final answer:
The system of equations 15x - 4y = 62 and 5x + 8y = 86 is solved using the method of elimination, yielding the solution x = 6 and y = 7.
Explanation:
We are asked to solve a system of equations:
15x - 4y = 625x + 8y = 86We will use the method of elimination to solve this system, which involves manipulating the equations so that adding or subtracting them will eliminate one of the variables, allowing us to solve for the other.
Multiply the second equation by 3: 15x + 24y = 258.Subtract the first equation from the modified second equation: 15x + 24y - (15x - 4y) = 258 - 62.This gives us 28y = 196, and solving for y gives us y = 7.Substitute y = 7 into the first original equation to find x: 15x - 4(7) = 62.Solve for x: 15x - 28 = 62, which gives x = 6.Therefore, the solution to the system of equations is x = 6 and y = 7.
Which expression is equivalent to 8/15?
A. 8÷1/5
B. 8÷15
C. 15÷1/8
D. 15÷8
Answer: B is the answer
Step-by-step explanation:
A group of students go out for lunch. If two have
hamburgers and five have hot dogs, the bill will be
$8.00. If five have hamburgers and two have hot dogs,
the bill will be $9.50. What is the price of a hamburger?
Answer:
1.50$
Step-by-step explanation:
2 hamburgers would equal 3$ and if the hot dogs are 1$ each it woul make the equation true
To find the price of a hamburger, set up a system of equations and solve for the price using the given information. So, the price of a hamburger is $2.50
Explanation:To find the price of a hamburger, we can set up a system of equations based on the given information.
Let x be the price of a hamburger.
From the first scenario, we have 2x + 5(0.50) = 8.00.
From the second scenario, we have 5x + 2(0.50) = 9.50.
Simplifying these equations gives us 2x + 2.50 = 8.00 and 5x + 1.00 = 9.50.
Solving these equations, we find that x = $2.50.
Therefore, the price of a hamburger is $2.50.
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The average score on the statistics final exam was 85 and the standard deviation was 2.5 . Chris scored a 95 . Chris scored higher than what percent of his class?
Answer:
55%
Step-by-step explanation:
its honestly just a guess
y = 0.0043x3 − 0.24x2 + 0.583x + 199.8
what does this look like graphed ?
Answer:
Table and graph attached
Step-by-step explanation:
Graph of a Function
Given a real function f(x), we can construct its graph by taking random values for x, computing f(x) for each selected value, and plotting the pairs (x,f(x)) in a rectangular grid. By joining the points we get an approximate graph.
It's not always easy to find an appropriate set of values for x which makes the important part of the graph be clearly shown in the graph. We select the range for x between -30 and +70. The results are shown in the table below.
The graph is also shown in the second image provided.
Find the value of x. Round to the nearest degree.
Select one:
a. 53
b. 37
c. 49
d. 39
Answer:
a. 53
Step-by-step explanation:
The side with length 15 is opposite the right angle, so it is the hypotenuse of the right triangle.
For angle x, the side measuring 12 is the opposite leg.
Our 3 items of interest are: angle, opposite leg, hypotenuse.
The trig ratio that relates the opposite leg to the hypotenuse is the sine ratio.
sin x = opp/hyp
sin x = 12/15
sin x = 0.8
Now we take the inverse sine of 0.8 to find the measure of the angle.
x = sin^(-1) 0.8 = 53 deg
Raj has a $25 budget to spend on decorations for a party he has already spent $18.60 he now wants to get some helium balloons that’s cost $0.80 each write and solve an inequality to show the number of balloons the raj could buy
Answer:
The number of balloons Raj could buy is 8.
Step-by-step explanation:
Given:
Raj has a $25 budget to spend on decorations for a party.
He has already spent $18.60.
He wants to get some helium balloons that’s cost $0.80 each.
Now, to write and solve an inequality to show the number of balloons Raj could buy.
Let the number of balloons be [tex]x.[/tex]
Cost of each balloons = $0.80.
So, the total cost of balloons = [tex]0.80x.[/tex]
He already spent = $18.60.
Total budget Raj has = $25.
Now, to solve an inequality to show the number of balloons:
[tex]0.80x+18.60\leq 25[/tex]
Subtracting both sides by 18.60 we get:
[tex]0.80x\leq 6.40[/tex]
Dividing both sides by 0.80 we get:
[tex]x\leq 8.[/tex]
Therefore, the number of balloons Raj could buy is 8.
Enter the unknown value that makes this statement true.
20% of ______ is 120
Answer:
20% of 600 is 120
Step-by-step explanation:
We shall use X as the variable
20% of x is 120
To find 20 percent of something, divide by 5.
Alternatively, you can find 10% of it then multiply by two.
600÷5 is 120
We see that 20% of 600 is 120
What is the next step in the construction of a regular hexagon?
Answer:
With compass setting the same as line segment PA, place the compass
at C and draw an arc that intersects the circle ⇒ answer D
Step-by-step explanation:
Lets revise the step of construction a regular hexagon
1. Draw circle with center P; put point A on the circle's edge at
any place
2. With compass setting the same as line segment PA, place the
compass at A and draw an arc that intersects the circle at B
3. With compass setting the same as line segment PA, place the
compass at B and draw an arc that intersects the circle at C
4. With compass setting the same as line segment PA, place the
compass at C and draw an arc that intersects the circle at D
5. Contain with the same step of placing the compass at the previous arc and draw an arc with same distance of PA until you reach point A again, then join each arc on the circle forming the regular hexagon
The given steps are:
Circle with center P; point A is along the circles edge, an arc at point B
is along the circles edge, and an arc at point C is along the circles edge
According to the steps above, the next step is:
With compass setting the same as line segment PA, place the
compass at C and draw an arc that intersects the circle (step 4)
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The next step will be to use a compass and a straight edge to draw the second equilateral triangle with side AB. Option B is correct
Given that,
To determine the next step in the construction of a regular hexagon.
What is a polygon?A polygon is defined as a geometric shape that is composed of 3 or more sides these sides are equal in length, and an equal measure of angle at the vertex,
Examples of the polygon, equilateral triangle, square, pentagon, etc
Here,
The next step is to draw a straight edge through the corresponding arc to the side AB, to form the second equilateral triangle.
Thus, the next step will be to use a compass and a straight edge to draw the second equilateral triangle with side AB. Option B is correct
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prove equal chord of a circle substend equal angle at centre
Answer:
The Proof for "Equal chord of a circle subtends equal angle at the Center".
Step-by-step explanation:
Consider a Circle with center as C,
Radius AC ,BC ,DC and EC
Chord AB = Chord CD
To Prove:
"Equal chord of a circle subtends equal angle at center".
i.e ∠ACB = ∠ECD Which are Center angle
Proof:
In Δ ABC and Δ DEC
Chord AB ≅ Chord DE .….{Given}
AC ≅ DC …..{Radius of Same Circle}
BC ≅ EC ….{Radius of Same Circle}
Δ ABC ≅ Δ DEC ….{By Side-Side-Side Congruence Postulate}
∴∠ACB ≅ ∠ECD ...{Corresponding Parts of Congruent Triangles are Congruent or CPCTC} ....Proved
i.e Equal chord of a circle subtends equal angle at the Center.