There are 210 sequences for 7 church bells to rung with the given conditions. Using permutations, the required number of sequences is calculated.
What are permutations?A sequence or arrangement that can be framed by taking some or all of a finite set of things (or objects) is called a permutation.
The formula for finding the number of such arrangements is,
ⁿPₓ = n!/(n - x)!
Calculation:It is given that, a church's bell tower has 7 bells. 3 of them will ring in a sequence before each service and no bell is rung more than once.
So, the number of sequences that the bells will form is calculated by using the permutations formula. I.e., ⁿPₓ = n!/(n - x)!
Here, n = 7; x = 3
Then,
ⁿPₓ = n!/(n - x)! ⇒ ⁷P₃ = 7!/(7 - 3)! = 7!/4!
⇒ ⁷P₃ = (7 × 6 × 5 × 4!)/4! = 7 × 6 × 5 = 210
Therefore, there are 210 sequences for ringing the bells.
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Jonathon has a cookies stand where customers may buy small packages of cookies and large boxes of cookies. Jonathon sold 3 small packages of
okies and 14 large packages of cookies for a total of $203. Lily sold 11 small packages of cookies and 11 large packages of cookies for a total of
220. Write and solve the system of equation.
Use x andy and the information provided to create two equations:
olve the system:
What is the cost of each small package of cookies?
What is the cost of each large package of cookies?
The cost of each small package of cookies is $7 and the cost of each large package of cookies is $11.
What is a variable?
Any qualities, quantity, or number that can be gauged or tallied qualifies as a variable. A data item is another name for a variable. Examples of variables include age, sex, company income and expenses, country of birth, capital expenditures, class grades, eye colour, and vehicle kind.
Given that the total cost of 3 small packages of cookies and 14 large packages of cookies is $203.
The total cost of 11 small packages of cookies and 11 large packages of cookies is $220.
Assume that the cost small packages of cookies is x and large packages of cookies y.
Then the cost of 3 small packages of cookies and 14 large packages of cookies is (3x + 14y).
The cost 11 small packages of cookies and 11 large packages of cookies is (11x + 11y).
The system of linear equation is
3x + 14y = 203 .....(i)
11x + 11y = 220 .....(ii)
Multiply equation (i) by 11 and equation (ii) by 3
33x + 154y = 2233
33x + 33y = 660
______________
121y = 1573
Divide both sides by 121:
y = 13
Putting y = 13 in equation (i)
3x + 14 × 13 = 203
3x = 21
x = 7
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rewrite 27 1/3 using roots
The value of the exponent illustrated as 27^1/3 is 3.
How to illustrate the exponent?The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.
In this situation, it should be noted that 27^1/3 simply means the cube root of 27. This will give a value of 3.
Check: 3 × 3 × 3 = 27.
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With 2.4 million digital subscribers, Game Informer Magazine (ranked first) has 1150% more digital subscribers than National Geographic (ranked third). How many digital subscribers does National Geographic have?
The number of subscribers of the third-ranked Magazine is 1116,279.
What is algebra?
One of the many branches of mathematics is algebra. Algebra, which is a common thread throughout practically all of mathematics, is broadly defined as the study of mathematical symbols and the rules for using these symbols in formulas.
Here, we have
Given
Number of digital subscribers = 2.4 million
Percentage increment = 1150%
Let x represent the number of subscribers the third-ranked magazine
The relationship between the number of subscribers of the top-ranked and third-ranked magazines is defined as follows;
2.4 million = x + 1150% of x
Convert to digits only
2,400,000 = x + 1150% * x ------- By reordering
x + 1150% * x = 2,400,000
x + 1150/100 * x = 2,400,000
x + 1.15 * x = 2,400,000
Now we Factorize
x(1 + 1.15) = 2,400,000
x (2.15) = 2,400,000
Now we Divide through by 2.15
x = 2,400,000/2.15
x = 1116,279.07
x = 1116,279
Hence, the number of subscribers of the third-ranked Magazine is 1116,279.
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At the gift shop, they sell small greeting cards and large greeting cards. The cost of a small greeting card is $2.05 and the cost of a large greeting card is $3.70. How much would it cost to get 5 small greeting cards and 4 large greeting cards? How much would it cost to get x small greeting cards and y large greeting cards?
It would cost $25.05 to buy 5 small and 4 large cards.
What is Total cost?
The total cost is the sum total of costs of individual items.
Given,
Cost of small card = $2.05
Cost of large card = $3.70
Therefore,
Total cost = total cost of small card + total cost of large cards
= 5*(2.05) + 4*(3.70)
= 10.25 + 14.8
= 25.05
Hence, It would cost $25.05 to buy 5 small and 4 large cards.
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Recall that two angles are complementary if the sum of their measures is 90°. Find the measures of two complementary angles if one angle is 15º more than two times the other angle. What does the smaller angle measure? What does the bigger one measure?
Answer:
smaller = 25, bigger = 65
Step-by-step explanation:
x = smaller
y = bigger
2x + 15 + x = 90
3x + 15 = 90
3x = 75
x = 25
y + x = 90
y + 25 = 90
y = 65
a triangle undergoes a dilation with a scale factor of 7/10. the resulting triangle is _[blank]_ the original triangle.
The resulting triangle is 7/10 the original triangle.
How triangle dilated with scale factor?The focuses in the direction planes are A(0, 2), B(2, 1), C(- 2, - 2). In the event that the scale factor is 2, each direction point of the first triangle is duplicated by the scale factor 2. Subsequently, the expanded triangle will be A'B'C' and the direction focuses got are A'(0, 4), B'(4, 2), C'(- 4, - 4).
According to question:Let we have a triangle ABC,If this triangle undergoes a dilation with a scale factor of 7/10,
Then changed triangle is A'B'C'
So, relation between them is A'B'C' = 7/10(ABC)
Thus, the resulting triangle is 9/5 multiple of triangle ABC.
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A grandfather has lived as many years as his grandson lived in months. His son has lived as many weeks as his grandson his lived days. If you add their ages, you would get 120 years. How old is the grandfather?
Two trains, each moving at 20 miles per hour towards each other, are initially 60 miles apart. A bee starts at the front of one train, flies to the other train, then back to the first train, and so on. If the bee always flies at 30 miles per hour, how far does the bee fly before the trains collide? Hint: For how long does the bee fly?
Answer:
45
Step-by-step explanation:
a certain test is worth 135 points. how many points (rounded to the nearest point) are needed to obtain a score of 85%?
To obtain a score of 85% on a test worth 135 points, one needs to get 115 points. By using proportions, we get the required value.
How to write proportions?A proportion is defined as an equality between two ratios.
Consider two ratios a:b and c:d. Then, the proportion we can write,
a: b = c : d
Then, the simplification we have for this proportion is
a/b = c/d or ad = bc
Calculation:It is given that, a certain test is worth 135 points.
One to get 85% on this test, he/she needs to get X number of points.
So, we can write the proportions as
X : 135 = 85 : 100
⇒ X/135 = 85/100
⇒ X = 85/100 × 135
∴ X = 114.75 ≅ 115 points
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Pls answer and show work
Step-by-step explanation:
always remember Pythagoras for right-angled triangles (90°) :
c² = a² + b²
c is the Hypotenuse (the baseline opposite of the 90° angle), a and b are the legs.
so, in our case
ramp² = 11² + 60² = 121 + 3600 = 3721
ramp = sqrt(3721) = 61 ft
Answer:
61 feet
Step-by-step explanation:
Because the triangle is a right triangle we can use the Pythagorean theorem to solve for the length of the ramp.
The Pythagorean theorem is a² + b² = c²
Where, a and b = leg lengths and c = hypotenuse (longest side)
Here, the length of the ramp represents the hypotenuse as it is the longest side. We are also given the length of the legs. The lengths being 60 ft and 11 ft.
This means that a and b = 11 and 60
We can plug these lengths in and then solve for c or the length of the ramp
a² + b² = c²
==> plug in a = 11 and b = 60
11² + 60² = c²
==> simplify exponents
121 + 3600 = c²
==> add 121 and 3600
3721 = c²
==> take the square root of both sides
61 = c
So the length of the ramp is 61 feet
can someone please explain this 4x[tex](4x^{2} -5x)- (4x^{2} -4x-8)[/tex]
the answer is -x+8 but I don't get why its +8 and not -8
Your first step of simplifying is to distribute the "–" or "–1" in front of the second set of parentheses through that second set of parentheses. The –1 must be distributed to every term in the second set:
[tex]\begin{aligned}(4x^2-5x)-(4x^2-4x-8)&=(4x^2-5x)\boldsymbol{{}-1}(4x^2-4x-8)\\[0.5em]&=4x^2-5x\boldsymbol{{}-1(4x^2)-1(-4x)-1(-8)}\\[0.5em]&=4x^2-5x\boldsymbol{{}-4x^2+4x+8}\\[0.5em]&=-x+8\\\end{aligned}[/tex]
That's what changes the sign on every term in the second set of parentheses, making that –8 become +8.
jamal wants to estimate the
distance across the gorge
shown in the diagram below.
He stands at point Y and
locates a tree at point X
directly across the gorge to the
north. He then walks west
along the gorge 500ft and
marks point A. After walking
another 500ft in the same
direction, he turns 90 degrees
and walks south, perpendicular
to the gorge. He stops when
his location appears to form a
straight line with points A and
X. Jamal measures the
distance BC as 327 ft. What is the distance of XY across the gorge?
Jamal's estimate of the distance across the gorge is 1424.56 ft
What is Pythagorean Theorem ?
The Pythagorean Theorem is a well-known geometric principle that states that the squares on the hypotenuse of a right triangle, which is the side opposite the right angle, equal the total of the squares on the legs.
First, he can draw a diagram to represent the situation. He can label points Y, X, A, and B on the diagram and draw the lines YX and AB to represent the locations of the tree and the points he marked.
Next, he can use the Pythagorean Theorem to find the distance AC. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the side AC is the hypotenuse, and the sides YA and YC are the other two sides. Therefore, he can use the theorem to find AC as follows:
AC^2 = YA^2 + YC^2
He knows the values of YA (500ft) and YC (327ft), so he can substitute these values into the equation and solve for AC:
AC^2 = 500^2 + 327^2
AC^2 = 250000 + 107649
AC^2 = 357659
AC = √357659
AC ≈ 597.56 ft
Finally, he can use the distance AC to estimate the distance across the gorge. The distance across the gorge is equal to the distance from X to Y, which is equal to the sum of the distances from X to A and A to Y. Therefore, he can estimate the distance across the gorge as follows:
distance across gorge = XA + AY
distance across gorge = AC + YA + YC
distance across gorge = 597.56 ft + 500 ft + 327 ft
distance across gorge ≈ 1424.56 ft
This is Jamal's estimate of the distance across the gorge.
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Ira ran out of time while taking a multiple-choice test and plans to guess on the last 666 questions. Each question has 444 possible choices, one of which is correct. Let x=x=x, equals the number of answers ira correctly guesses in the last 666 questions. What is the probability that he answers fewer than 222 questions correctly in the last 666 questions?.
It is possible to calculate the probability that in the last 6 questions, there were fewer than 2 right answers, which is 53.392%.
What is Probability?The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x.
The probability of an event can be calculated using the following formula.
Probability(Event) = Positive Results/Total Results = x/n
In order to better grasp probability, let's look at a straightforward application.
Let's say we need to forecast if it will rain or not. Either "Yes" or "No" is the appropriate response to this query.
There is a chance that it will rain or not. Here, probability can be used. Using probability, one may forecast the results of a coin toss, a roll of the dice, or a card draw.
According to our question-
The likelihood that responses to fewer than two of the final six questions were right can be calculated using the procedure below:
There are 6 questions with a total of 4 possible answers, hence the value of p is:
The following formula provides the probability:
The following formula is used to calculate the likelihood that Ira would properly answer exactly 1 of the final 6 questions:
P(X = 1) = 0.35595
P(X = 0) = 0.17797 gives the likelihood that Ira will correctly answer 0 out of the final 6 questions.
Accordingly, the likelihood that the last 6 questions' answers contain fewer than 2 valid responses is: P = 0.17797 + 0.35595.
P = 0.53392
P = 53.392%
Hence, the probability that in the last 6 questions, there were fewer than 2 right answers, which is 53.392%.
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List 5 rational number between -4/7 and -3/8
pls answer
The five rational numbers between - 4 / 7 and - 3 / 8 by discretizing the set of rational numbers are - 181 / 336, - 85 / 168, - 53 / 112, - 37 / 84, - 137 / 336.
How to determine 5 possible rational numbers
Rational numbers are real numbers of the form m / n, where m and n are integers and n is a non-zero number. In this case, we need to determine five numbers between two given rational numbers: - 4 / 7, - 3 / 8.
Since there is an infinite set of rational numbers, we must create an additional criterion to discretize that set and find the five required numbers more easily. This can be done by means of the following formula:
y = a + (b - a) · [x / (n + 1)]
Where:
a - Lower bound.b - Upper bound. n - Index of the number.If we know that a = - 4 / 7, b = - 3 / 8 and n = 5, then the five rational numbers are:
n = 1
y = - 4 / 7 + [- 3 / 8 + 4 / 7] · (1 / 6)
y = - 181 / 336
n = 2
y = - 4 / 7 + [- 3 / 8 + 4 / 7] · (2 / 6)
y = - 85 / 168
n = 3
y = - 4 / 7 + [- 3 / 8 + 4 / 7] · (3 / 6)
y = - 53 / 112
n = 4
y = - 4 / 7 + [- 3 / 8 + 4 / 7] · (4 / 6)
y = - 37 / 84
n = 5
y = - 4 / 7 + [- 3 / 8 + 4 / 7] · (5 / 6)
y = - 137 / 336
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if s ( m ) represents the salary (per month), in hundreds of dollars, of an employee after m months on the job, what would the function r ( m )
The function r ( m ) $12 more than the salary of someone who has worked for m months.
What is function?
A function is a type of rule that produces one output for a single input. Source of the image: Alex Federspiel. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would say that y is a function of x.
If we have S(m) represents salary after m months i.e. y=S(m) will be the graph of salary Corresponding to the number of months m.
So, we have [tex]m+12 \geqslant 12$,[/tex]
[tex]$\Rightarrow S(m+12)$[/tex] will give us the value of Salary after 12 months of the Job.
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PLEASE ANSWER FAST y-1/6=15/18
In parallelogram lonm, what is om? 7 cm 17 cm 24 cm 34 cm
In parallelogram lonm, om is 34.
What is parallelogram?
A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of equal size.
A quadrilateral with the opposing sides parallel is called a parallelogram. A parallelogram with all right angles is known as a rectangle, and a quadrilateral with equal sides is known as a rhombus.
First we have OQ =QM,
So 2x+3=3x-4,
x =7.
Hence OM =2(17)=34.
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Answer: D) 34
Step-by-step explanation:
edge 2023
1.1\times 10^{4}1.1×10
4
in standard form.
The number 1.1 * 10⁴ in standard form is 11000
How to determine the number in standard formFrom the question, we have the following parameters that can be used in our computation:
Number = 1.1\times 10^{4}1.1×104
Rewrite the given number properly
So, we have the following representation
Number = 1.1 * 10⁴
Solving further, we need to apply the law of indices to expand the exponents
Using the above as a guide, we have the following:
Number = 1.1 * 10 * 10 * 10 * 10
Evaluate the product of the 10's
So, we have the following representation
Number = 1.1 * 10000
Evaluate the products of the 1.1 and 10's
So, we have the following representation
Number = 11000
Hence, the number is 11000
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Use compatible numbers to estimate the correct quotient.
The value of quotient will be;
⇒ 60
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The expression is,
⇒ 15 ) 900 (
Now,
Solve the expression by dividing, we get;
⇒ 15 ) 900 ( 60
- 90
--------
× 0
Thus, The value of quotient will be;
⇒ 60
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extended Response
1. The weights of grapefruits, 0, of a certain variety are approximately Normally
distributed with a mean of 1 pound and a standard deviation of 0.12 pounds.
a. Let 7-36. Find the mean and standard deviation of 7.
b. Let R= G+G+G. Find the mean and standard deviation of R.
c. Let Q=T-R. Find the mean and standard deviation of Q.
The mean weight of 7 grapefruits will be 7 pounds and the standard deviation will be 0.84 pounds.
The mean weight of R will be 3 pounds and the standard deviation will be 0.36 pounds.
The mean weight of Q will be 4 pounds and the standard deviation will be 0.48 pounds.
What is the mean and standard deviation?a. The mean and standard deviation of 7 grapefruits will be 7 times the mean and standard deviation of a single grapefruit, respectively.
b. If G represents the weight of a single grapefruit, then
R = G + G + G
= 3G.
The mean and standard deviation of R will therefore be 3 times the mean and standard deviation of a single grapefruit, respectively.
c. If T represents the total weight of all 7 grapefruits, then
Q = T - R
= 7G - 3G
= 4G.
The mean and standard deviation of Q will be 4 times the mean and standard deviation of a single grapefruit, respectively.
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Charles has 12 coins in his pocket. Some are nickels and some are quarters. If the value of the coins is $2.20, write a system of equations that could be used to find the number of nickels and quarters Charles has in his pocket. Let n represent nickels and q represent quarters. Select the two equations that represent the system of equations described above.
The equations representing the number and value of coins are n + q = 12 and 5n + 25q = 2.20 respectively.
What is a system of linear equations?A system of linear equations is a group of equations having same number of variables and degree.
For the n number of variables n number of equations are required.
On the basis of number of solutions a system of equations can be classified as consistent and inconsistent.
The given problem can be solved as follows,
Suppose the number of nickel and quarter coins are n amd q respectively.
Then, the equation for the total number of coins can be written as,
n + q = 12 (1)
And, the equation for their value is given as,
5n + 25q = 2.20 (2)
Hence, the two equations that can be used to represent the given case are n + q = 12 and 5n + 25q = 2.20 respectively.
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Find the function rule for g(x).
9. The function f(x)=-6x. The graph of g(x) is f(x) vertically stretched by a factor of 7 and reflected in the x-axis. What is the function rule for g(x)?
Answer:
The function rule for g(x) can be obtained by performing the transformations described on the function f(x) = -6x.
First, we need to stretch the graph of f(x) vertically by a factor of 7. This means that the y-values of the points on the graph of g(x) will be 7 times the y-values of the points on the graph of f(x). We can achieve this by multiplying the y-values of the function f(x) by 7.
Next, we need to reflect the graph of g(x) in the x-axis. This means that the y-values of the points on the graph of g(x) will be the negative of the y-values of the points on the graph of f(x). We can achieve this by multiplying the y-values of the function f(x) by -1.
Applying these transformations to the function f(x) = -6x, we get the function rule for g(x) as follows:
g(x) = (-1) * (7) * (-6x)
= (-1) * (-42x)
= 42x
Therefore, the function rule for g(x) is g(x) = 42x.
An object moving in a circle is represented by the motion map. An illustration of a circle with four black dots on the top labeled w, bottom labeled y, left labeled z and right labeled x of the circle. Each dot has a vector toward the center of the circle of equal length and a vector tangent to the circle in a counterclockwise direction of equal length. Based on the map, at which point is the object accelerating toward the right? w x y z.
The required point at which point is the object accelerating toward the right is Z.
Explain centripetal force.A force following up on a moving body at a point to the bearing of movement, having a tendency to cause the body to follow a round or ended way. The power of gravity following up on a satellite in circle is an illustration of a centripetal power; the rubbing of the tires of a vehicle making a turn comparatively gives centripetal force on the vehicle.
According to question:The item in the guide is moving by round movement: consequently, there is a force (called centripetal force ) that pulls the item towards the center point of the circle.
As indicated by Newton's law motion,
F = ma
a power on the item relates to a speed increase, and this speed increase (called centripetal speed increase) has a similar course of the power. Thus, since the speed increase is towards the focal point of the circle also, the main place of the direction where the speed increase is towards the right is at point Z.
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A student with a poor understanding of straight-line graphs writes down some incorrect information
next to each equation. Decide how the error might have been made and then correct the information.
X-2y=4. (Gradient=1)
Answer:
½
Step-by-step explanation:
The coefficient of x is 1 but the equation is not in the form of y = mx + b
x - 2y = 4
-2y = 4 - x
2y = x - 4
y = ½x - 2
Therefore, the gradient is ½
help me lord pls pls
Answer:
.5l means that you are going to add 1/2 cups of lemon juice for every bath that you make. If you made one batch, you would use 1/2 of lemon juice. If you made 2 batches you will add 1 cup of lemon juice and so on.
2s means that you will add 2 cups of sugar for each batch. If you made one batch, you would add 2 cups of sugar, if you made 2 batches you would add 4 cups nd so on.
Step-by-step explanation:
Point C is the midpoint of line segment AB and point B is between points A and D. If AD = 20 and BD =12 then what is CD?
Answer:
16
Step-by-step explanation:
AB = 20 - 12 = 8
BC = 8 : 2 = 4
CD = 4 + 12 = 16
Answer:
CD = 16
Step-by-step explanation:
Check the image for the steps
Solve each system by elimination: 3x-8y=13 4x-5y=6
Answer:
Your answer is [tex]x = -1[/tex] and [tex]y = -2[/tex]
Step-by-step explanation:
(attached)
The diameter of a circle is 11 cm. Find its area to the nearest tenth.
The area of the given circle is 95 cm².
What is a circle?All points in a plane that are at a specific distance from a specific point, the center, form a circle.
In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.
So, we know that the diameter of the circle is 11 cm.
Radius = Diameter/2
11/2
5.5 cm
Area of circle: πr²
3.14(5.5)²
3.14*30.25
94.985
Rounding off: 95 cm²
Therefore, the area of the given circle is 95 cm².
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A toy jeep i 12 and 1/2 inche long while an actual jeep meaure 18 3/ 4 feet long what i the value of the ratio length of the toy jeep to the length of the actual Jeep what doe thi ratio mean in the ituation?
Therefore the solution of this question is ratio length = every 1 inch of toy car represents 1.5 feet of actual car
What is ratio?In mathematics, a ratio shows how two numbers are multiplied together. In a bowl of fruit, for instance, the proportion of oranges to lemons is eight to six if there are eight oranges and six lemons. Lemons to oranges are divided 6:8 and oranges to all other fruits are divided 8:14 in a similar fashion.
Here,
A toy Jeep measures 12 1/2 inches.
Before calculating the ratio, let's first convert each size into the same unit of measure and decimal points:
=>12 ½ = 25/2
=> 12.5 inches;
=> 18 ¾ = 75/4
=> 18.75 feet .
The actual length of a jeep is 18.75 feet.
The ratio can now be determined by converting feet to inches.
1 inch of a toy car equals 1.5 feet of an actual car because
=> 1 foot = 12 inches
=> 12.5 inches : 225 inches
=> 225 / 12.5
=> 18 inches
Therefore, every 1 inch of toy car represents 1.5 feet of actual car.
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An animal shelter currently only has 30 dogs and 20 cats. What is the ratio of cats to animals?
Answer:
20:50 or 2:5
Step-by-step explanation:
30 dogs
20 cats
50 total animals
Part to whole relationship:
20:50