The standard form of the equation of the circle is (x-5)² + (y+3)² = 9² and the general form is x² + y² + 10x + 6y - 47 = 0 .
We know that the general form of the equation of a circle is given by the following equation:
(x-h)² + (y-k)² = r² . Where r is the radius of the circle and (h, k) is the center of the circle.
So the general equation of the circle is (x-5)² + (y+3)² = 9² .
Let's first define a circle in order to determine its equation. A circle is formed by every point in a plane that is uniformly spaced from another point.
The constant point is located at the center of the circle. The radius of a circle is the separation between its center and any point along its circumference.
(x-5)² + (y+3)² = 9²
or, x² + 10x + 25 + y² + 6y + 9 = 81
or, x² + y² + 10x + 6y - 47 = 0
Hence the general form of the circle is x² + y² + 10x + 6y - 47 = 0.
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Thomas has $10 to spend on lunch. He decides to buy come chicken sandwiches, which cost $2 each, and one container of orange juice, which cost $1.50. What is the greatest number of chicken sandwiches that Thomas can buy?
Solve each given equation and show your work. Tell whether it has one solution, an infinite number of solutions, or no solutions, and identify each equation as an identity, a contradiction, or neither.
A) 6x + 4x - 6 + 24 + 9x
B) 25 - 4x = 15 - 3x +10 - x
C) 4x + 8 = 2x + 7 + 2x - 20
(i) The value of x is equal to 30 and the equation has one solution and it is neither identity nor contradiction.
(ii) This equation has infinite number of solutions and it is an identity.
(iii) This equation has no solutions and it is a contradiction.
What is identity and contradiction?
An identity is an equation that can be solved using any integer that can replace the variable in the equation in a meaningful way. A conditional equation is one that is met by some numbers but not by others, such as 2x = 4. A contradiction is an equation, such as x = x + 1, that cannot be solved.
We know that,
An equation having infinitely many solutions is called an identity equation.
An equation that having no solution is called a contradiction.
(i) 6x + 4x - 6 + 24 + 9x
Combining like terms
x = 30
Therefore, The value of x is equal to 30 and the equation has one solution and it is neither identity nor contradiction.
(ii) 25 - 4x = 15 - 3x +10 - x
Combining like terms
0 = 0
It means, The equation is true for all values of x.
Therefore, This equation has infinite number of solutions and it is an identity.
(iii) 4x + 8 = 2x + 7 + 2x - 20
Combining like terms
8 = -13
It means, The equation is not true for any value of x.
Therefore, This equation has no solutions and it is a contradiction.
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Jan is five years older than Tom in three years time will be 3/4 as old is Jan what is Tom's age now
The present age of Tom is 12 years old
Jan is five years older than Tom
The age of Tom = x
The age of Jan = x + 5
After 3 years
The age of Tom = x + 3
The age of Jan = x + 5 + 3
= x + 8
The Tom's age is 3/4 of Jan's age
Then the equation will be
x + 3 = 3/4(x + 8)
Apply distributive property
x + 3 = (3/4)x + 6
x - (3/4)x = 6 - 3
Subtract the terms
1/4 x = 3
Move 1/4 to the right hand side of the equation
x = 3 ÷ 1/4
x = 3 × 4
Multiply the terms
x = 12 years old
Hence, the present age of Tom is 12 years old
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a =? , b = 40 ft , C = 50 ft
Answer:
a = 30
Step-by-step explanation:
I am not exactly sure what the question is asking but if referring to right triangles, the Pythagorean theorem would work best.
Formula :
[tex]a^2 + b^2 = c^2\\\\[/tex]
Substitute values :
[tex]a^2 + 40^2 = 50^2\\a^2 + 1600 = 2500[/tex]
Solve for a:
[tex]a = \sqrt{2500 - 1600} \\a = 30[/tex]
** you could also use the 3:4:5 ratio
1.3 x 10 to the power of negative 3
Answer:0.0013
Step-by-step explanation:
Answer: the answer is on the calclulator
Step-by-step explanation:
SOMEONE PLEASE HELPPPPPPPPPPPP!
Given: (GH) is a midsegment of ∆DEF. Show all work.
Find the value of x and y.
What is the length of (DF)?
In the given ΔDEF x is 17 units and y is 2 units.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
Given, GH is the midpoint of ΔDEF and EF is the base of the ΔDEF with a length of 28 units.
We know the midpoint of ΔDEF is (1/2) EF.
∴ GH = (28/2) = 14 units.
Now GH = x - 3.
14 = x - 3.
x = 17.
Given DH and FH are equal.
∴ y + 8 = x - 7.
y + 8 = 17 - 7.
y + 8 = 10.
y = 2.
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A spice mixture is 25% thyme. How many grams of thyme must be added to 12g of the mixture to increase the thyme content to 40%?
Answer:
3 g
Step-by-step explanation:
You want to know the mass of thyme that must be added to 12 g of a spice mix that is 25% thyme in order to make it 40% thyme.
SetupLet t represent the amount of added thyme (in grams). The amount of thyme in the augmented mix is ...
0.25(12) + t = 0.40(12 +t)
SolutionSimplifying the equation gives ...
3 +t = 4.8 +0.40t
0.6t = 1.8 . . . . . . . . . subtract 0.40t +3
t = 3 . . . . . . . . . . . divide by 0.6
3 grams of thyme must be added to the mix.
Line of best fit
Correlation coefficient
Intercept r
Find y when x=12
Considering the given scatter plot, it is found that:
a. The line of best fit is: y = -0.245x + 5.59.
b. The correlation coefficient is: r = -0.57.
c. The interpretation of the correlation coefficient is of: There is a negative association between y and x.
d. The estimate of y when x = 12 is of: 2.65
What is a scatter plot?A scatter plot is a set of points of a data-set, and these points are used to calculate both the correlation coefficient and the line of best fit.
For this problem, the points are given as follows:
(0,5), (1,7), (2, 6), (3, 4), (4, 3), (5,5), (6,4), (7,2), (8,5), (9,3), (10,4).
Inserting these points into a linear regression calculator, the line of best fit is given as follows:
y = -0.245x + 5.59.
Hence the estimate of y when x = 12 is obtained as follows:
y = -0.245(12) + 5.59 = 2.65.
Inserting these points into a correlation coefficient calculator, the correlation coefficient is given as follows:
r = -0.57.
The interpretation is that there is a negative association between y and x, which is neither strong neither weak, as the absolute value of the coefficient is close to the threshold of 0.6.
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Two identical rectangles linked at one corner are drawn on coordinate axes. Give the coordinates of point A and point B
The coordinates of the vertices of the points A and B are;
A(9, 7), B(15, 9)
What is the location of a point on the coordinate plane?A point on the coordinate plane is described by a pair of points known as an ordered pair.
The coordinates of the vertices of the identical rectangles are; (3, 5), (9, 5), (9, 9)
The length of (9 5) from A is the same as the length from (9, 9) to A.
The coordinate of the point A is therefore;
x-coordinate = 9
y-coordinate = 5 + (9 - 5)/2 = 7
The coordinate of point A is (9, 7)
The length of the sides of the rectangle are;
Length = 9 - 3 = 6
Width = 9 - 7 = 2
The coordinates of the point B are;
x-coordinate = 9 + 6 = 15
y-coordinate = 9
The coordinates of the point B is (15, 9)
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I'm very stuck on this problem, mainly because of how restricted the selection of proofs is, and if you can help or give ideas I would really appreciate just listening to your thoughts on the question, thank you!
Check the picture below.
so in the parallelogram, the two triangles split by the side AC are congruents as you can see there by AAS, that means their sides and angles are congruent, that also includes the exterior angles.
since the exterior angles are also congruent, we can extend lines BC and AD as you see there in green and run an exterior angle at vertices A and C, since those two exterior angles are congruent and are also alternate interior ones, voila! it must be that BC || AD.
1. A candle weighs 300 grams (g). Each hour the candle is lit, it burns 4 g of its wax. a. Leth be the number of hours the candle burns. Write an equation that can be used to determine the number of hours it takes for the candle to weigh 206.4 g. b. Solve the equation to determine the number of hours it takes for the candle to weigh 206.4 g. Show your work.
Please help me tomorrow I Will hace a test about this question!!
Answer:
Step-by-step explanation:
300 grams-24 hour= 276 so i think u just need to keep doing this till it gets to 206.4
The equation which represents the number of hours will be ln(206.4) = 1200ln(0.014).
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a candle weighs 300 grams (g). Each hour the candle is lit, it burns 4 g of its wax. a. Leth be the number of hours the candle burns.
The equation for the number of hours will be calculated as,
[tex]h=300\times (0.014)^h[/tex]
lnh= 300 x ln(0.014)
Therefore, the equation which represents the number of hours will be ln(206.4) = 1200ln(0.014).
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1. If two expressions with exponents are a perfect match except one has a negative exponent and
the other has a positive exponent, like 53 and 5-3, how does the exponent change the meaning
of the expression?
According to the law of exponent, the value of positive exponent is greater than the negative exponent, this defines that they are not equal.
Exponent
Exponent refers the number of times a number is multiplied by itself.
Given,
Here we need to verify that, if two expressions with exponents are a perfect match except one has a negative exponent and the other has a positive exponent, like 5³ and 5⁻³, then how does the exponent change the meaning of the expression.
According to the following law of the exponent, the positive exponent can be written as,
5³ = 5 x 5 x 5 = 125
Similarly, the negative exponent is written as,
5⁻³ = 1/5³
Which can be simplified as,
1/125 = 0.008
Therefore, when we compare these values, the value of positive exponent is greater than the negative exponent.
Thus, defines that the value of positive and negative exponent are not same.
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**BRAINLEST**, **THANKS** AND **5 STARS** TO WHOEVER ANSWERS CORRECT FIRST! PLEASE HELP ME OUT THIS IS FOR ALGERBRA 2/PRE-CALCULUS
- During a certain time of year, the daily temperature in a certain city, in degrees Celsius follows a periodic pattern. The graph below shows the temperature over two days, where time t is measured in hours after 12:00 a.m. (midnight) on the first day.
- Write an equation for the graph below in terms of Y (temperature in degrees Celsius) and T (time in hours) to represent the given context.
- ANSWER SHOULD LOOK LIKE THIS FORMULA
y = ( a ) sin ( b ) (t - h) + k
- IF YOUR STILL UNCLEAR, THE SECOND SCREENSHOT IS WHAT THE ANSWER SHOULD LOOK LIKE
- (NO, THAT SECOND PHOTO WITH THE FORMULA ISNT THE ANSWER!!!!!)
GRAPH IS GIVEN BELOW PLEASE HELP ME OUT! ILL GIVE BRAINLIEST VOTE 5 STARS AND GIVE THANKS IF YOURE CORRECT AND FAST!!!! PLEASE HELP ME OUT
The sinusoidal equation for the graph in terms of Y, the temperature in degrees Celsius) and the time, T in hours is; Y = 3·sin((π/12)·(T + 6)) + 15
What is a sinusoidal equation?A sinusoidal equation or function is an oscillating and periodic function that is based on the sine of an angle.
The required form of the response is y = a·sin(b·(t - h)) + kThe function of the graph is a sinusoidal function with the parts;
a = The amplitude
b = The frequency = 1/T
T = The period of the function
k = The vertical shift of the function
h = The horizontal shift of the function
From the graph, we have;
The minimum point on the graph of the function = (1, 12)
The maximum point on the graph of the function = (13, 18)
The amplitude of the graph a is therefore; a = (18 - 12)÷2 = 3
The period of the graph = 1/b
1 cycle is completed in 24 hours, which indicates that the frequency of the function is; f = 2·π/24 = π/12 = b
The vertical shift, k from the parent function, y = sin(x) which is the distance the midline of the graph is raised above the x-axis is; k = 15
sin((π/12)·(0 - h)) = -1
((π/12)·(0 - h)) = -π/2
-h = 6
h = -6
The function, y = a·sin(b·(t - h)) + k, is therefore;
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A construction worker earns an average bi-weekly net pay of $1,764.00. Which compound inequality correctly shows the amount of money, t, the worker can spend if the monthly budget for food is between 10% and 20%?
$176.40 ≤ t ≤ $352.80
$352.80 ≤ t ≤ $706.50
$382.20 ≤ t ≤ $764.40
$420.42 ≤ t ≤ $573.30
The compound inequality is $176.40 ≤ t ≤ $352.80 if a construction worker earns an average bi-weekly net pay of $1,764.00 option (A) Is correct.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
It is given that:
A construction worker earns an average bi-weekly net pay of $1,764.00.
= 10% of 1764
= (10/100)1764
= $176.4
= 20% of 1764
= (20/100)1764
= $352.8
Inequality will be: $176.40 ≤ t ≤ $352.80
Thus, the compound inequality is $176.40 ≤ t ≤ $352.80 if a construction worker earns an average bi-weekly net pay of $1,764.00 option (A) Is correct.
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Answer:
$382.20 ≤ t ≤ $764.40
Step-by-step explanation:
Hello, so first we would need to convert bi-weekly pay to monthly income.
First we would times $1,764.00 by 26
1764.00 × 26 = 45864
Then we would divide 45864 by 12
45864 ÷ 12 = 3822.
Then we calculate how much the worker can spend if their monthly budget for food is in between 10% and 20%
3822 × 10% = 382.20
3822 × 20% = 764.40
So, we can see the correct answer is $382.20 ≤ t ≤ $764.40.
Once an antibiotic is given, number of bacteria decreases at a rate of 15%/day. There were about 15,000 bacteria prior to the treatment. The graph models the number of bacteria after x days of treatment.
What are the key features of the exponential function modeled in terms of this situation and how can they be interpreted?
Select each correct answer.
The line y = 0 is an asymptote of the graph.
The x-intercept is 30.
The line x = 0 is an asymptote of the graph.
The asymptote indicates that there will never be more than 15,000 bacteria.
The y-intercept is 15,000.
The y-intercept represents the number of bacteria when treatment began.
The asymptote indicates that as time increases, the number of bacteria approaches 0.
The key features of the exponential function modeled in terms of this situation and how can they be interpreted are;
1) The y-intercept is 15,000.
2) The y-intercept represents the number of bacteria when treatment began.
3) The asymptote indicates that as time increases, the number of bacteria approaches 0.
What are the key features of the exponential function Graph?The general formula for an exponential function is;
y = aˣ
Now, an asymptote of a curve is defined as a line that exists in a way that the distance that exists between the curve and the line approaches zero as either one or both of the x or y coordinates approaches to infinity.
From the given graph, we can say that the y-intercept which is where the curve intersects the y-axis is 15,000 and this indicates the number of bacteria that existed prior to treatment.
The asymptote of the graph would likely be around x = 1 and it indicates that as time increases, the number of bacteria approaches 0.
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A firm makes circular drink mats , of radius 4.5cm , that are 3mm thick . They want to produce a rectangular box to hold a pile of 12 mats. What are the minimum dimensions of the box.
write answer and working out no spamming
Answer: The minimum is 13.5
Step-by-step explanation:
But if I got to multiply the 12 also it will be 162
Divide 2/3 by 8/15. Simplify your answer
Answer:
5/4
Step-by-step explanation:
(2/3)/(8/15)
= (2/3)(15/8)
= (2*15)/(3*8)
= 30/24
= 5/4
The correct answer is: " [tex]\frac{5}{4}[/tex] " ; {written as an improper fraction} ;
or: " 1.25 " ; {written as a decimal value} ;
or: " [tex]1\frac{1}{4}[/tex] " ; {written as a mixed number fraction}.
__________________
Step-by-step explanation:
Given: [tex]\frac{2}{3}[/tex] ÷ [tex]\frac{8}{15}[/tex] = ? {for which we shall solve}.
Note: 'Dividing by' a value; results in the same value as 'multiplying by' its reciprocal value [that is: 'multiplying by its inverted form'].
This is especially noteworthy in problems that involve 'dividing by fractions'.
So, to solve and simply our given problem:
[tex]\frac{2}{3} * \frac{15}{8}[/tex] = ? ;
Note: The 2 cancels out to 1 ; and the 8 cancels out to 4 ;
The 3 cancels out to 1 ; and the 15 cancels out to 5 ;
→ since: {8 ÷ 4 = 2 } ; & {2 ÷ 2 = 1} ;
and :
→ since: {15 ÷ 3 = 5 } ; & {3 ÷ 3 = 1 } .
______
We can rewrite our "further simplified" expression as:
→ [tex]\frac{1}{1}[/tex] * [tex]\frac{5}{4}[/tex] ;
= " 1 * [tex]\frac{5}{4}[/tex] " ;
= " [tex]\frac{5}{4}[/tex] " .
Further explanations:
1) Note: Re: the "commutative property" of multiplication:
" a * b = b * a " ; or, write as: " ab = ba " ;
As such: " 1 * \frac{5}{4} " ; is the same as:
↔ " [tex]\frac{5}{4}[/tex] * 1 " .
2) Note: Re: the identity property of multiplication:
Any value, multiplied by "1", results in/ retains its same value}.
As such; our calculated value:
" [tex]\frac{5}{4}[/tex] * 1 " = \frac{5}{4} " .
3) Note: Re: the division of one (1) property of division:
Any value, divided by "1" ; results in that same initial value.
As such: our calculated value: " [tex]\frac{1}{1}[/tex] = (1 ÷ 1) = 1 " ;
4) Note: Re: the division by itself property of division:
Any value (except "0"), divided by itself, is equal to "1 " ;
As such: our calculated value: " [tex]\frac{1}{1}[/tex] = (1 ÷ 1) = 1 " ;
______
So, this answer—which is the most simplified, improper fraction—
is: " [tex]\frac{5}{4}[/tex] " .
Or, to write as a mixed fraction:
Use the mnemonic:
[tex]\frac{n}{d}[/tex] = M [tex]\frac{a}{d}[/tex] ;
That is: "numerator/denominator = M( [tex]\frac{a}{d}[/tex] )" ; {"M a/d" !} l
⇒ in which M is the [calculated singular whole number portion within the mixed number equivalent] ;
⇒ followed by " [tex]\frac{a}{d}[/tex] " ; in which d is the same denominator as that of the improper fraction ;
⇒ & in which a is the calculated numerator value for the fraction portion for this number ;
So: " \frac{5}{4}} " = (5 ÷ 4) = 1.25 = 1 [tex]\frac{1}{4}[/tex] " .
______
Long division method:
__________________________________________
1 R 1 ; ⇒ 1 + (1/4) ; that is; " 1 + (remainder) / (divisor)";
4⟌5 → 1 + ( 1 / 4) ;
− 4 = " 1 [tex]\frac{1}{4}[/tex] ".
1 ; So, " [tex]1\frac{1}{4}[/tex] " ; as a mixed number fraction.
or: Use a fraction calculator to convert improper fractions into mixed number fractions.
________________________
or: Use a calculator: " {5 ÷ 4} = 1.25 " .
____
The correct answer is: " [tex]\frac{5}{4}[/tex] " ; {written as an improper fraction} ;
or: " 1.25 " ; {written as a decimal value} ;
or: " [tex]1\frac{1}{4}[/tex] " ; {written as a mixed number fraction}.
____
Hope this answer is helpful!
Wishing you the best!
____
Write the equation in slope-intercept form.
3x + 6y = 18
y =
=x + [
Answer:
Slope intercept form is achieved by isolating y to one side. 3x-6y=18: given. -6y=-3x+18: algebra. y=3/6x-3: simplifying.
The volume of 10,000 drops of a liquid is 10 fluid ounces.
What is the volume of 10 drops?
Answer: .01 fluid ounces.
Step-by-step explanation:
1,000 drops is 1 FL
100 drops is .1 FL
10 drops is .01 FL
A blue rope is two times as long ad a red rope. A green rope is 8 times as long as the blue rope. If the total length of three ropes is 708.75 meters, what is the length of the blue rope?
Answer: b ≈ 74.605 meters
Step-by-step explanation:
Let b be the length of the blue rope, r be the length of the red rope, and g be the length of the green rope. We will write different equations to show the situation given.
b = 2r
g = 8b
b + r + g = 708.75 meters
Next, we will substitute expressions into the last equation for the variables r and g so we can solve for b.
b + r + g = 708.75 meters
b + ([tex]\frac{b}{2}[/tex]) + (8b) = 708.75 meters
9.5b = 708.75 meters
b ≈ 74.61 meters
b ≈ 74.605 meters
Pat and Fran are quality control specialists in a
light bulb factory. Pat inspects every 20 cartons
of bulbs for breakage. Fran inspects every 36
cartons for incorrect labeling. If they start at
the same time, which carton will be the first
that both of them inspect?
Answer:
Carton 180Step-by-step explanation:
This is about the LCM of the numbers 20 and 36.
First find the prime factors of both numbers:
20 = 2*2*536 = 2*2*3*3Now find the LCM:
LCM(20, 36) = 2*2*3*3*5 = 180They will both inspect every 180 cartons.
Answer:
They will both inspect every 180 cartons.
Step-by-step explanation:
Firstly you could find the LCM of 20 and 36.
Multiples of 20 are: 20, 40, 60, 80, 100, 120, 140, 180, etc...
Multiples of 36 are: 36, 72, 108, 144, 180, 216, 252, 288, etc...
Therefore 180 is the answer, all they were asking was what was the LCM. Hope this helped you !!
Mrs.Josey and her family were taking a trip to Dallas to go to the Botanical Gardens.If the trip was a total of 350 miles one way and their car can go 20 miles on one gallon of gas, how many gallons will they need to make it to Dallas
The number of gallons of gas which Mrs. Josey and her family would need is; 17.5 gallons of gas.
How much gas is needed to make it to Dallas?It follows from the task content that the quantity of gas in gallons needed by Mrs. Josey and her family to make it to Dallas is to be determined.
Therefore, since one gallon of gas is enough for 20 miles, It follows that the amount of gas required for 350 miles can be determined by proportion as follows;
20/1 = 350/x
x = 350 / 20
x = 17.5 gallons of gas.
Ultimately, the amount of gas needed for Mrs. Josey and her family to make it to Dallas is; 17.5 gallons of gas.
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help plss
Write the description of each transformation in the order of operations.
Answer: PEMDAS
Parenthesis exponents multiplication Division addition subtraction
Step-by-step explanation:
solve (x+1) first then after just follow pemdas
Divide:
4⁄6 ÷ 2⁄6 =
..
Answer:2
Step-by-step explanation: I don’t have a explanation
Answer: 2
Step-by-step explanation:
You should be able to do this...
Trucks in a delivery fleet travel a mean of 130 miles per day with a standard deviation of 37 miles per day. The mileage per
normally Find the probability that a truck drives at least 63 miles in a day. Round your answer to four decimal places.
Hurry
The probability that a truck drives at least 63 miles in a day is 0.9649
How to find the required probabilityThe probability is solved using z scores, this measures the amount of standard deviation sample X is from mean.
the formula is below
z = (X - μ) / σ
Definition of variables
mean, μ = 130 miles per day
standard deviation, σ = 37 miles per day
X = 63 miles per day
score, z
substituting into the formula
= (X - μ) / σ
= (63 - 130) / 37
= -1.81081 the p value for = 0.035085
the probability is calculated to be 1 - 0.035085 = 0.9649
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One month before a stock car race, the sale of ads for the official race program was slow. Only 24 pages, or just 40% of the available pages, had been sold. Find the total number of pages devoted to advertising in the program.
Answer: 60 pages
Step-by-step explanation: 24 pages time 2 would be 48 pages, which is 80% of the pages. Since 12 pages is 20%, you would add 12 pages, which equals 60 pages.
i'm lost on this question can i please get someones help! thanks
Answer:
infinite
Step-by-step explanation:
A bell rings every 1/6 hour. Assuming it just rang, how many times will it ring in the next 2/3 hour?
A baseball player makes an annual salary of 3,200,000. and makes $17,260.274 a day.
A charitable organization states that for $120 it can send 1 child to school in a developing country for 1 year . The baseball player decides to donate 10% of his annual salary to this organization .
Calculate 10% of the baseball player’s salary.
Answer:
320,000.00
Step-by-step explanation:
use the drop down menus for 5−4+7+1
Answer:
9
Step-by-step explanation:
5 - 4 + 7 + 1 = 9/1 = 9