The scale factor is 3/2. The length of XY is 18.
What are similar Quadrilaterals?
Two figures are said to be similar if they share the same shape. Congruent objects are those that are precisely the same size and shape. Real-world examples of congruent figures or objects include, for instance, both of a person's hands, both of a car's front wheels, etc.
If the corresponding angles and sides of two quadrilaterals are equal, then the two quadrilaterals are similar.
Given that Quadrilateral ABCD is similar to Quadrilateral WXYZ.
Thus
AB/WX = BC/XY = CD/YZ = AD/WZ ....(i)
The length of AB = 15, BC= 27, WX= 10
The scale factor is
AB/WX = BC/XY = CD/YZ = AD/WZ
= 15/10
= 3/2 [Divide the denominator and numerator by 5]
Take first two ratios of (i):
AB/WX = BC/XY
15/10 = 27/XY
3/2 = 27/XY
XY = 27 × (2/3)
XY = 18
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1) Write the equation of the line passing through point P with slope m, if
a) P(1,4) and m = 3
c) P (3,0) and m = −1
b) P(-1,-2) and m = 4
d) P(0,0) and m = -5
Answer:
a) y - 4 =3(x - 1)
b) y + 2 = 4(x+ 1)
c) y = -(x - 3)
d) y = -5x
Step-by-step explanation:
You did not say which form, so I put them in the point-slope form of a line that follows the pattern:
y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex])
Answer:
see explanation
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
(a)
given m = 3 , then
y = 3x + c ← is the partial equation
to find c substitute (1, 4 ) into the partial equation
4 = 3(1) + c = 3 + c ( subtract 3 from both sides )
1 = c
y = 3x + 1 ← equation of line
(b)
given m = 4 , then
y = 4x + c ← is the partial equation
to find c substitute (- 1, - 2 ) into the partial equation
- 2 = 4(- 1) + c = - 4 + c ( add 4 to both sides )
2 = c
y = 4x + 2 ← equation of line
(c)
given m = - 1 , then
y = - x + c ← is the partial equation
to find c substitute (3, 0 ) into the partial equation
0 = - 3 + c ( add 3 to both sides )
3 = c
y = - x + 3 ← equation of line
(d)
given m = - 5 , then
y = - 5x + c ← is the partial equation
to find c substitute (0, 0 ) into the partial equation
0 = - 5(0) + c = 0 + c ⇒ c = 0
y = - 5x ← equation of line
each of two persons tosses three fair coins. what is the probablity they obtain same number of heads
The probability of obtaining the same number of heads is 3/8 or 0.375 when each of two persons tosses three fair coins.
The probability that two persons will obtain the same number of heads depends on the number of possible combinations of heads and tails that can be obtained by each person.
Since each coin flip results in either a heads or tails, there are 2 possible outcomes for each flip. Therefore, for three coin flips,
there are 2^3 or 8 possible combinations of heads and tails.
Out of these 8 combinations, there are 3 in which both persons have the same number of heads (i.e., 0 heads, 1 head, or 3 heads).
So, the probability of obtaining the same number of heads is 3/8 or 0.375.
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Find y in equilateral AABC. (A) 90° (B) 70° (C) 60° (D) 45°
Variable y in equilateral 60°, Thus correct option is C) 60°.
What does an equilateral triangle mean?An equilateral triangle is one with equal-sized sides on all three sides and angles that can all reach a maximum of 60 degrees. An equilateral triangle is a triangle with three equal sides, also referred to as a "regular" triangle. Since all three sides of an isosceles triangle are equal, an equilateral triangle is a special case of an isosceles triangle. Three equal angles of 60 degrees also make up an equilateral triangle.
The sum of all the angles in a triangle is 180.
It is given that the triangle ABC is an equilateral triangle.
So ∠A+∠B+∠C =180°
∠A=B=∠C
3∠A=180°
∠A=60°
Therefore y in ΔABC is C) 60°
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The side length of a square is( 2/3g+1) cm. Use this information to complete parts (a) and (b)
The perimeter of a square with length of a side given as 2/3g + 1 cm is 8/3g + 1 cm.
Let's call the length of a side of the square "s". According to the information given, s = 2/3g + 1 (in cm).
The perimeter of a square is equal to the sum of the lengths of all four sides, so we can write an expression to represent the perimeter as follows:
P = 4s
Substituting the expression for s from above, we get:
P = 4(2/3g + 1)
So, the expression for the perimeter of the square in terms of g is:
P = 4(2/3g + 1)
Therefore, P = 8/3g + 1.
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Complete question: the length of a square is( 2/3g+1)cm use this information to write an expression to represent the perimeter of the square.
please answer asap i need helpp
Answer:
110°
Step-by-step explanation:
]%}}%¶¢{^[€{¢¶¢¶€¶
Answer: 110˚
Step-by-step explanation:
Complementary angles have a sum of 90˚
With this knowledge, we can say <B = 90 - <A = 90 - 20 = 70˚
Supplementary angles have a sum of 180˚
With this knowledge we can say <C = 180 - <B = 180 - 70 = 110˚
∴ Measure of angle C = 110˚
7 plums cost 63p
5 limes cost 60p
work out the cost of 1 plum
The cost of one plum in pence is 9p. The cost of 1 lime in pence is 12p.
Comparing the cost plum is cheaper.
The cost of 1 plum can be found by dividing the total cost of 7 plums by 7:
63 p / 7 = 9 p
Therefore, the cost of 1 plum is 9 p.
The cost of 1 lime can be found by dividing the total cost of 5 limes by 5:
60 p / 5 = 12 p
Therefore, the cost of 1 lime is 12 p.
Comparing the costs of 1 plum and 1 lime, we see that 1 plum costs 9 p and 1 lime costs 12 p. Therefore, the plum is cheaper per item.
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____The given question is incomplete, the complete question is given below:
A grocery shop sells plums and limes. 7 plums cost 63 p. 5 limes cost 60p a) Work out the cost of 1 plum, in pence (p).
b) Work out the cost of 1 lime, in pence (p).
c) Which type of fruit is cheaper per item?
a circular table is painted yellow with a red square in the middle. the radious of the tabletop is 6x. the side length of the red square is 3x. what is the area of the yellow part of the tabletop.
PLS HELP!!! I NEED IT FOR LESS THAN 20 MINUTES
Answer:
51 stamps
Step-by-step explanation:
since salman's amount is going from 5 to 45 its being multiplied by nine. to keep the ratio true, you need to multiply the other two numbers by 9 too. Nathan then has 12 stamps and Gordon has 63. 63-12=51
express 2x^2 + 8x in the form a(x + b)^2 + c
The vertex form equivalent to the given expression; 2x² + 8x as required to be determined in the task content is; 2 (x + 2)² + 8.
What is the vertex form equivalent of the expression?The vertex form equivalent of the given expression can be determined as follows;
2x² + 8x
2 (x² + 4x)
2 ( (x + 2)² + 4)
= 2 (x + 2)² + 8.
Ultimately, the vertex form equivalent of the given expression as required is; 2 (x + 2)² + 8.
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Pleas help with this homework
Using substitution method, the value of x and y are -13/3 and 2/3 respectively
What is system of linear equationA system of linear equations is a set of two or more linear equations with the same variables. The solution to the system is the set of values for the variables that satisfies all of the equations simultaneously. The variables represent unknown values that we are trying to solve for, and each equation provides a constraint on those variables.
To find the value of x and y, we can use substitution method.
4x + 8y = 12 ...eq(i)
x + 2y = -3 ...eq(ii)
From eq(ii)
x = -3 + 2y ...eq(iii)
Put eq(iii) into eq(i)
4(-3 + 2y) + 8y = 12
-12 + 8y + 8y = 12
-12 + 16y = 12
16y = 24
y = 2/3
Put y = 2/3 in eq(ii)
x + 2(2/3) = - 3
x + 4/3 = -3
x = -13/3
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% of $52 = $39 ?
Complete the following statement. Write your answer as a decimal or whole number.
Answer:
75%
Step-by-step explanation:
If you have a calculator, you can divide 39/52. If not,
39/52 = x/100
52x = 3900
x = 75
75/100 = 75%
The image of a trapezoid is shown.
An isosceles trapezoid with a short base of 3 meters and a height of 5.8 meters. The portion of the large base from the left vertex to the perpendicular is 4 meters. The portion of the large base from the right vertex to the perpendicular is 7 meters.
What is the area of the trapezoid?
The area of the trapezoid would be 42.5 m².
What is the area of a trapezoid?
The area of a trapezoid is given by the formula:
Area = (1/2) × (sum of the bases) × height
where the bases are the two parallel sides of the trapezoid and the height is the perpendicular distance between the bases.
The parameters of the trapezoid are;
Short base length = 3 m
Height = 5
Large base length = 4 + 3 + 7 = 14 m
Thus;
Area of a trapezoid = 1/2 * (Short base + Large base) * h
Area = 1/2 * (3 + 14) * 5
= 1/2 * 17 * 5
= 42.5 m²
Hence, the area of the trapezoid would be 42.5 m².
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Rewrite the equation in Ax+By = C form.
Use integers for A, B, and C.
y-2=-5(x-3)
Answer:
5x + y = 17
Step-by-step explanation:
y -2 = -5(x -3)
y-2 = -5x + 15 Add 5x to both sides
5x + y - 2 = 5x - 5x + 15
5x + y - 2 = 15 Add 2 to both sides
5x + y + 2 - 2 = 15 + 2
5x + y = 17
a poll is given, showing 61% are in favor of a new building project. let x be the number of people who favor the new building project when 25 people are chosen at random. what is the distribution of x? x ~ ? (,) please show the following answers to 4 decimal places. what is the probability that exactly 16 people out of 25 favor the new building project? what is the probability that at least 16 people out of 25 favor the new building project? what is the probability that at most 16 people out of 25 favor the new building project? what is the probability that between 12 and 19 (including 12 and 19) people out of 25 favor the new building project?
The probability that exactly 16 people out of 25 favor the new building project is 0.1285.
The probability that at most 16 people out of 25 favor the new building project is 0.3528.
The probability that between 12 and 19 (including 12 and 19) people out of 25 favor the new building project is 0.9088.
A binomial distribution is a probability distribution that describes the number of successes in a fixed number of trials, where each trial has two possible outcomes (success or failure) and the trials are independent.
The distribution of x, the number of people who favor the new building project when 25 people are chosen at random, can be modeled using a binomial distribution.
In this case, the probability of success (favoring the new building project) is 0.61, and the probability of failure (not favoring the project) is 0.39. The number of trials is 25, since we are choosing 25 people at random.
Thus, we can write x ~ Bin(25, 0.61), which means that x follows a binomial distribution with 25 trials and a probability of success of 0.61.
To find the probability that exactly 16 people out of 25 favor the new building project, we can use the binomial probability formula:
[tex]P(X = k) = (^n_k) * p^k * (1 - p)^{n - k}[/tex]
where X is the random variable (in this case, the number of people who favor the project), k is the number of successes we are interested in (in this case, 16), n is the number of trials (25), p is the probability of success (0.61), and (n choose k) is the binomial coefficient, which represents the number of ways to choose k successes out of n trials.
Plugging in the values, we get:
P(X = 16) = (25 choose 16) * 0.61¹⁶ * 0.39⁹ = 0.1285
Therefore, the probability that exactly 16 people out of 25 favor the new building project is 0.1285.
To find the probability that at least 16 people out of 25 favor the new building project, we need to add up the probabilities of all the events where the number of successes is 16 or greater. We can do this using the cumulative distribution function (CDF) of the binomial distribution, which gives us the probability of X being less than or equal to a certain value.
Using a calculator or a table, we can find that P(X ≥ 16) = 0.3528.
Therefore, the probability that at least 16 people out of 25 favor the new building project is 0.3528.
To find the probability that at most 16 people out of 25 favor the new building project, we can use the complement rule, which states that the probability of an event occurring is equal to 1 minus the probability of its complement (the event not occurring). In this case, the complement event is the number of people who favor the project being greater than 16.
Using the same CDF, we can find that P(X > 16) = 0.6472. Therefore,
P(X ≤ 16) = 1 - P(X > 16) = 1 - 0.6472 = 0.3528
We can do this using the binomial probability formula for each possible value of k, and then summing the results.
P(12 ≤ X ≤ 19) = P(X = 12) + P(X = 13) + ... + P(X = 19)
Using a calculator or a table, we can find the probabilities for each value of k, and then add them up:
P(12 ≤ X ≤ 19) = 0.0309 + 0.0746 + 0.1322 + 0.1821 + 0.2001 + 0.1821 + 0.1322 + 0.0746 = 0.9088
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с A F E 2x In the diagram above JED= 27°." 1) Calallate I G B солав, angle angle EG B
Angle A is 27 degrees, angle B is 75 degrees then the angle C is 78 degrees.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Let the triangle be ABC.
The angle A is 27 degrees.
The angle B is 75 degrees,
We need to find the angle of C
From Angle sum property the sum of three angles is 180 degrees.
∠A+∠B+∠C=180
27+75+∠C=180
102+∠C=180
∠C=78 degrees.
Hence, angle A is 27 degrees, angle B is 75 degrees then the angle C is 78 degrees.
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Complete Question below:
In Triangle ABC, angle A is 27 degrees, angle B is 75 degrees then the angle C?.
A plane is flying at a speed of 175 miles per hour.
The pilot plans on flying at this speed for the next
250 miles, plus or minus 25 miles. Find
the minimum and maximum number of hours th
plane will travel at that speed.
The maximum number of hours is 1.6 hours and the minimum number of hours is 1.6 hours.
What is the speed?The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.
Given that, a plane is flying at a speed of 175 miles per hour.
The distance covered by the pilot, d = 250 ± 25 miles
We know that, speed = Distance/Time
The equation for the maximum number of hours is given as;
175 =(250+25)/t
t=275/175
t=1.6 hours
The equation for the minimum number of hours is given as;
175 =(250-25)/t
175=225/t
t=225/175
t=1.3 hours
Therefore, the maximum number of hours is 1.6 hours and the minimum number of hours is 1.6 hours.
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Please answer ASAP What is the value of x? Enter your answer, as a decimal, in the box. Enter the numerical value only.
In the similar triangle, x = 67.5 ft
What are similar triangles?Similar triangles are triangles in which the ratio of their sides are equal.
How to find the value of x?Given the similar triangles, ΔMNP and ΔMAB
By the ratio of similar triangles, we have that
MP/MN = MB/MA
We observe that MN = MA + AN
So, MA = MN - AN
So, MP/MN = MB/MA
MP/MN = MB/(MN - AN)
Given that
MP = 97.5 FT, MN = 71.5 FT, AN = 22 FT and MB = xWe have that
MP/MN = x/(MN - AN)
Making x subject of the formula, we have that
x = (MN - AN)MP/MN
So, substituting the values of the variables into the equation, we have that
x = (MN - AN)MP/MN
x = (71.5 ft - 22 ft)97.5 ft/71.5 ft
x = 49.5 ft × 97.5 ft/71.5 ft
x = 4826.25 ft²/71.5 ft
x = 67.5 ft
So, the value of x = 67.5 ft
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What is another way to make 2.98?
Choose 1 answer:
B
1 one +8 tenths +18 hundredths
1 one 19 tenths 8 hundredths
1 one +10 tenths 8 hundredths
Answer:
Below
Step-by-step explanation:
1 + 19/10 + 8/100 = 1 + 1.9 + .08 = 2.98
These tables represent the relationships between x and y for two different sets of data. Which statements correctly describe the relationships between x and y for each table? Table A represents a multiplicative relationship because y is 2.5 times x, O and Table B represents an additive relationship because y is 2 more than O X. Table A represents an additive relationship because y is 1.5 more Othan x, and Table B represents a multiplicative relationship because y is 3 times x. Both data sets represent multiplicative relationships. In Table A, y is 2.5 times x, and in Table B, y is 3 times X. Both tables represent additive relationships. In Table A, y is 1.5 more than x, and in Table B, y is 2 more than x.
Answer:
Both data sets represent multiplicative relationships. In Table A, y is 2.5 times x, and in Table B, y is 3 times X
Step-by-step explanation:
Self-explanatory
Every value of y in Table A is 2.5 times x value
and
every value of y in table B is 3 times x value
A pyrotechnician plans for two fireworks
to explode together at the same height In the air. They travel
at
speeds shown below. Firework B is launched 0.25 s before Firework A. How many seconds after
B Firework B launches will both fireworks explode?
Firework A
Firework B
340 ft/s
260 ft/s
The mentioned scenario can be calculated using the distance equation, the number of seconds in which explosion would occur is 1.125 seconds.
What is the relationship between time, speed and distance ?The distance covered by the object is equal to the product of the speed of object and the time required for it.
Distance = Time x speed
Firework A :
D = 360xt - - - (1)
Firework B:
D = 280x(0.25) + 280xt
D= 70 + 280xt - - - (2)
Equate equation (1) and (2) :
360t = 280t + 70
Collect like terms
360t - 280t = 70
80t = 70
t = 70/80
t = 0.875 seconds
0.875 + 0.25 = 1.125 seconds
Hence, the fireworks will explode after 1.125 seconds of launching Firework B.
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8. Gianna is making bows for her cheerleading squad. She has 4 yards of ribbon to make the
bows. If each bow requires 1/5 a yard of ribbon, will she have enough ribbon to make 18 bows?
Using the concept of proportion, Gianna will have enough yards to make 18 bows
Will she have enough ribbon to make 18 bowsTo solve this problem, we need to apply the concept of proportions.
In order to make 1 bow, she needs 1/5 yard of ribbon
Representing this in an equation form will be;
1 bow = 1/5 yard
18 bow = x yard
cross multiply both sides and solve for x
x * 1 = 18 * (1/5)
x = 3.6 yards
From the above, there will be enough yards to make 18 bows.
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solve the equation 4x+2y-8=0
Answer:
X=0
Y=4
Step-by-step explanation:
4X+2y-8=0
2y=4x+8
y=2x+4
Substituting y in the equation
4x+2(2x+4)-8=0
4x+4x+8-8=0
8x=0
X=0
Substituting in equation y=2x+4
y=2(0)+4
Y=4
Tanner is 2 years younger than his
brother. Tanner's age t in years is 2
less than his brother's age b.
dependent variable:
independent variable:
equation:
The equation will be:
t = b - 2
And we can see that:
independent variable = brother's age.dependent variable = Tanner's age.How to identify the variables?Here we have two variables:
t = taner's age
b = age of Tanner's brother.
The independent variable is the one that does not depend on the other, in this case (for how it is worded) is the brother's age.
The dependent variable depends on the other, on this case, Tanner's age.
Now let's write the equation, we know that Taner's age is 2 years less than his brother, then:
t = b - 2
That is the equation.
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a researcher records the following data: 4, 4, 4, 4, and 3. how would you describe the variability of these data? group of answer choices it is negative because 3 is less than the other scores in the distribution. it is very small (close to 0) because scores are approximately the same. it is very large (much greater than 0) because 3 is an outlier in the data. it is equal to zero because scores are approximately the same.
The variability of the data is very small (close to 0) because all the scores are approximately the same.
The variability of these data can be calculated using the variance formula, which is the average squared difference from the mean. In this case, the mean is 3.8 (the sum of 4, 4, 4, 4, and 3 divided by 5). Therefore, the variance is 0.08 (the sum of the squared differences [4-3.8, 4-3.8, 4-3.8, 4-3.8, 3-3.8] divided by 5). This indicates that the variability of the data is very small (close to 0) because all the scores are approximately the same.
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Factorise 3y²+12y ‼️‼️‼️
Answer:
3y(y + 4)
Explanation:
[tex]3y^{2} + 12y\\3(y^{2} + 4y)\\3y(y + 4)\\[/tex]
You are using a recipe to bake some
cookies. The recipe calls for the following
ingredients:
3 3/4 cups flour
1 1/4 cups brown sugar
2 eggs
1/4 teaspoon salt
1/3 teaspoon baking soda
1 1/4 butter
1 1/2 cups white sugar
You've decided to only make 1/2 a batch.
How much of each ingredient do you need?
The required measurement of the ingredient has been shown below for half a batch of cookies.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
When making 1/2 a batch of the cookie recipe, you will need to halve the amount of each ingredient.
Here is the list of ingredients for half a batch:
1 7/8 cups flour
5/8 cup brown sugar
1 egg
1/8 teaspoon salt
1/6 teaspoon baking soda
5/8 cup butter
3/4 cup white sugar
Thus, the required measurement of the ingredient has been shown above for half a batch of cookies.
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Phillips company bought 40 percent ownership in jones bag company on january 1, 20x1, at underlying book value. During the period of january 1, 20x1, through december 31, 20x3, the market value of phillips' investment in jones' stock increased by $2,000 each year. In 20x1, 20x2, and 20x3, jones bag reported the following: Year Net Income Dividends
20X1 $ 8,000 $15,000 20X2 12,000 10,000 20X3 20,000 10,000 The balance in Phillips Company’s investment account on December 31, 20X3, was $54,000.
Required:
In each of the following independent cases, determine the amount that Phillips paid for its investment in Jones Bag stock assuming that Phillips accounted for its investment by carrying the investment at fair value, or using the equity method.
Fair value $
Equity method $
The initial investment cost using the equity method would be:
Investment account balance + Phillips' share of retained earnings = Initial investment cost = $54,000 + $10,400 = $64,400
Fair Value Method:
The cumulative increase in fair value over the three years would be:
$2,000 + $2,000 + $2,000 = $6,000
Therefore, the initial investment cost would be:
$54,000 - $6,000 = $48,000
Equity Method:
By the equity method, Phillips would have recorded its share of Jones Bag's earnings each year, as well as its share of dividends received. Phillips' share of Jones Bag's earnings and dividends would be based on its 40% ownership interest.
Phillips' share of Jones Bag's earnings and dividends would be as following:
Year Earnings Dividends
20X1 $3,200 $6,000
20X2 $4,800 $4,000
20X3 $8,000 $4,000
$40,000 - $14,000 = $26,000
Phillips' share of retained earnings would be 40% of $26,000, or $10,400.
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Solve for X
This was on a Geometry Honors quiz
The value of x in the triangle is 8 units.
How to find the side of similar triangle?Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
Therefore, the sides x of the triangle can be found using proportion as follows:
x / x + 8 = x + 8 / 32
cross multiply
32x = (x + 8)(x + 8)
32x = x² + 8x + 8x + 64
x² + 16x - 32x + 64 = 0
x² - 16x + 64 = 0
Therefore,
x² - 16x + 64 = 0
x² - 8x - 8x + 64 = 0
x(x - 8) - 8(x - 8) = 0
(x - 8)(x - 8) = 0
Therefore,
x = 8
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Julius went fishing on Saturday morning. He took a cooler to store the fish that he caught. The cooler could hold less than 8 large fish. Write an inequality that represents how many fish the cooler could hold.
8 > f
8 < f
8 ≥ f
8 ≤ f
Answer:
8 < f
8 must be strictly lesser than f, not greater than or equals to.
1. suppose that the students in your class want to have a party at which they will serve punch to drink. the punch the students want to serve is sold in half-gallon containers. if 25 students attend the party and if each student drinks 8 fluid ounces of punch, then how many containers of punch will you need? describe two different ways students could correctly solve this problem. for each method of solving the problem, explain simply and clearly why the method makes sense.
As per the volume, we need to to purchase 4 containers of punch.
To calculate the amount of punch required, we need to find the total volume of punch needed, which can be calculated as follows:
Total volume of punch = number of students * volume of punch per student
= 25 * 8 fluid ounces
= 200 fluid ounces
Now, we know that the punch is sold in half-gallon containers. One gallon is equal to 128 fluid ounces. Therefore, a half-gallon container is equal to 64 fluid ounces. We can use this information to find out how many containers of punch are needed:
Number of containers of punch = Total volume of punch / Volume of punch per container
= 200 / 64
= 3.125
Since we cannot purchase a fractional number of containers, we need to round up to the nearest whole number. Therefore, we need to purchase 4 containers of punch.
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