Answers
By using the definition of inverse functions we can see that:
a) g(7) = -10
b)(-10,7) is a point on h(x).
c)(7, -10) is a point on j(x)
How to evaluate the functions?Remember that if two functions f(x) and g(x) are inverses, then:
f(y) = x
g(x) = y
And also g(f(x)) = x = g(f(x)).
Here we know that functions h(x) and j(x) are inverses, and we also know that:
h(-10) = 7
So for the input -10, we have the output 7.
Then, by using the relation written above, we know that for the inverse function we must have:
j(7) = -10
That is the answer for a.
And for b and c the notation is (input, output), then:
(-10, 7) is a point on h.(7, -10)is a point on jThese are the answers of points B and C of the question.
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Related Questions
suppose you have 4 pairs of socks and 4 pairs of shoes. if you can wear any combination of socks and shoes, including mismatched pairs, how many different possible footwear choices can you make
Answers
There are a total of 32 different possible footwear choices that we can make.
Given, The number of pairs of socks = 4
The number of pairs of shoes = 4
We are to find out the number of possible footwear choices we can make if we can wear any combination of socks and shoes, including mismatched pairs.
So, We can wear any pair of socks with any pair of shoes including a mismatch.
Thus, for each pair of socks, there are 4 possible pairs of shoes.
And for each pair of shoes, there are 4 possible pairs of socks.
Therefore, we can form,
Total number of possible footwear choices = 4 pairs of socks * 4 pairs of shoes * 2 (considering the case of mismatched pairs) = 32 pairs.
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Interpreting data (Box & Whisker & Histogram) & Review Systems
For questions 1-4 use the graph below to answer the following questions/problems.
1. What is the value of the third quartile shown on the box-and-whisker plot?
2. Determine the interquartile range? Determine the range?
3. How many people were surveyed?
12
4. What is the type of average you can find? Find that average.
Answers
The type of average that can be found is the median. The median is the middle value of the data set when the values are arranged in order. In this case, the median is 11, as shown by the line inside the box.
What is value ?Value is the relative worth, merit, or importance of something. It is subjective and can be determined by a variety of factors, including personal preferences, beliefs, and economic forces. Value is a concept that can be applied to many different aspects of life, including economic goods, personal relationships, and objects. Value is determined by how much someone is willing to pay for something or how much someone needs something. In economics, value is determined by the market, which is based on supply and demand. In personal relationships, value is determined by the mutual respect, trust, and understanding between two people. In objects, value is determined by the sentiment and meaning it holds for the owner. Ultimately, value is a perception of worth, and its true value is subjective.
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After we planted flowers in 2/5 of our garden, 24m squared remained unplanted. How many square meters is this garden in total? if the total area of the garden is 1 the proportion of the remaining area is?
Answers
Thus, total garden area calculated in square meters is found to be 40 sq. m.
Explain about the one-variable linear equation?If the degree n in the equation is equal to 1, then a linear equation only contains ONE variable. The highest exponent a single variable can have is referred to as the equation's degree. Any arbitrary variable, such as x, y, or z, may be used as long as the linear equation is homogeneous.
Given data:
Let x be the total area of land.
Area of planted flowers : 2/5 x
Remaining area = 24 sq. m.
Thus,
Total area = Area of planted flowers + Remaining area
x = 2/5 x + 24
x - 2/5 x = 24
(5 -2)/5 x = 24
3x/5 = 24
x = 24*5 / 3
x = 8*5
x = 40
Thus, total area of the garden calculated in square meters is found to be 40 sq. m.
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how many ways are there to seat six people around a cir- cular table where two seatings are considered the same when everyone has the same two neighbors without re- gard to whether they are right or left neighbors?
Answers
the number of distinct seating arrangements when two seatings are considered the same when everyone has the same two without neighbors regard to whether they are right or left neighbors is:5!6⋅2=10.6⋅25! = 10
There are $(6-1)! = 5! = 120$ ways to seat six people around a circular table if the seatings are considered distinct. However, we must divide this number by $6$ to account for the fact that rotations of the same seating arrangement are considered the same. We also must divide by $2$ to account for the fact that reflections (i.e., reversing the order of people) of the same seating arrangement are also considered the same.
Therefore, the number of distinct seating arrangements when two seatings are considered the same when everyone has the same two neighbors without regard to whether they are right or left neighbors is:
5!6⋅2=10.6⋅25! = 10
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PLEASE HELP SOMEONE NEED TO DRAW A NUMBER LINE!!!
Answers
Answer=30 I think
Step-by-step explanation:
Blue card chances: 5/25=%20 Afterwards: 4/25=%16/2=%8
Red card chances: 12/25=%48 Afterwards: 11/25=%44/2=%22
Green card chances: 8/25=%32
Red and Blue card chances: %68
Answer=30 I think
what is the approximate probability that the actual proportion requiring aid will exceed that value? (round your answer to four decimal places.)
Answers
The approximate probability that the actual proportion requiring aid will exceed 0.08 is 0.5 (or 50%) rounded to four decimal places.
Given: The number of members in town = 400
The number of members requiring aid = 32
The proportion of members requiring aid = (number of members requiring aid) / (total number of members) = 32 / 400 = 0.08
To find the approximate probability that the actual proportion requiring aid will exceed this value, we need to assume a distribution for the proportion of members requiring aid. Assuming a normal distribution, we can use the Central Limit Theorem to approximate the sampling distribution of the sample proportion.
The standard error of the sample proportion is given by:
SE = √[p(1-p)/n]
where p is the population proportion and n is the sample size.
Substituting the values, we get:
SE = sqrt [(0.08 × 0.92) / 32] = 0.043
To find the probability that the actual proportion requiring aid will exceed 0.08, we can standardize the distribution using the z-score formula:
z = (x - p) / SE
where x is the value of the proportion we are interested in, p is the population proportion, and SE is the standard error of the sample proportion.
Substituting the values, we get:
z = (0.08 - 0.08) / 0.043 = 0
The probability that the actual proportion requiring aid will exceed 0.08 is equal to the probability of observing a z-score greater than 0, which is 0.5 (or 50%).
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The question is -
The towing service in town contracts with the club to come to the aid of up to 32 members in the next 12-month period. What proportion is that of the 400 members in town? .08 What is the approximate probability that the actual proportion requiring aid will exceed that value? (Round your answer to four decimal places.)
If Pythagoras, the Greek mathematician, was born in 582 BCE and died on his birthday in 497 BCE, how old was he when he died?
Answers
Born: 582 BCE
Died: 497 BCE
582-497= 85
Answer: 85 years old
Han is cycling at a speed of -8 miles per hour; if he starts at the same zero point what will his position be after 45 minutes?
Answers
Answer:
3.6 miles
Step-by-step explanation:
hope this helps!
(Picture included)
The table shows the results for spinning the spinner 50 times. What
is the relative frequency for the event "spin a 2"?
Experiment Table
Outcome 1 2 3 4
Frequency 12 10 10 18
Number of Trials
50
The relative frequency for the event "spin a 2" is:
(Simplify your answer)
Answers
The relative frequency for the event "spin a 2" is 1/5.
What is the relative frequency?Relative frequency measures how often a value appears relative to the sum of the total values.
In order to determine the relative frequency of spinning a 2, divide the frequency of spinning a two by the total number of trials.
Division is the process of determining the quotient of two or more numbers. It entails grouping a number into equal parts using another number. The sign that is used to represent division is ÷.
Relative frequency = number of times a two was spun / total number of trials
= 10 / 50 = 1/5
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i need help i cant figure out math
Answers
Answer:
See below.
Step-by-step explanation:
to find the change in temperature from 2:00 PM to 10:00 PM, you need to subtract the final temperature from the initial temperature. In other words,
Change in temperature = Final temperature - Initial temperature
In your problem, the final temperature is -9°F and the initial temperature is 18°F. Therefore,
Change in temperature = -9°F - 18°F
Change in temperature = -27°F
So, the change in temperature from 2:00 PM to 10:00 PM is -27°F.
The prices of petrol in a British and an American
petrol station are shown below.
The conversion rate is $1 = £0.80
What is the price of 1 litre of petrol in the cheaper
petrol station?
Give your answer in pounds (£).
British petrol station
£13.20 for 12 litres
of petrol
American petrol station
$17 for 20 litres
of petrol
Answers
The price of 1 liter of petrol at the cheaper petrol station is £0.68.
What is the conversion rate?
Just dividing the number of conversions by the total number of ad interactions that can be linked to a conversion within the same time period yields the conversion rate. Your conversion rate would be 5%, for instance, if you had 50 conversions out of 1,000 interactions, as 50 divided by 1,000 equals 5%.
Here, we have
Given: The prices of petrol in a British and an American petrol station are shown below. The conversion rate is $1 = £0.80.
We have to find the price of 1 liter of petrol in the cheaper petrol station.
$1 = £0.80
= £13.20×($1/£0.80)
= $16.5
For British petrol station
12 liter of petrol = $16.5
1 liter = $16.5/12
1 liter = $1.375
For American petrol station
20 liters of petrol = $17
1 liter = $17/20
1 liter = $0.85
The price of cheaper petrol from American petrol stations = $0.85× (£0.80/$1)
= £0.68
Hence, the price of 1 liter of petrol at the cheaper petrol station is £0.68.
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the two figures shown are made of unit squares. what is the positive difference of the perimeters, in units?
Answers
The two figures shown are made of unit squares. The positive difference of the perimeters, in units, is 8.
Perimeter is the total distance around the boundary of the shape. Since each square has a side length of 1 unit, the perimeter is equal to the number of sides.
1. Figure A: Counting the number of unit squares on the boundary of the shape, the perimeter of the first shape is: 8+4+4+4+4=24 units.
2. Figure B:Counting the number of unit squares on the boundary of the shape, the perimeter of the second shape is: 10+2+10+2=24 units.
The positive difference of the perimeters in units = |24 - 24| = 0 units. Therefore, the positive difference of the perimeters, in units is 0.
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tickets for a raffle cost 5. there were 833 tickets sold. one ticket will be randomly selected as the winner, and that person wins 1400 and also the person is given back the cost of the ticket. for someone who buys a ticket, what is the expected value (the mean of the distribution)?
Answers
The expected value (the mean of the distribution) for someone who buys a ticket can be calculated by adding up the total amount of money in the raffle and then dividing that by the number of tickets sold, which in this case in $6.68.
In this scenario, a ticket costs $5. The prize for winning the raffle is $1400 plus the cost of the ticket, which is $5.
The total value of the raffle is equal to the sum of the prize and the total amount of money raised from the tickets. The amount raised from the tickets is the number of tickets sold multiplied by the cost of the ticket.
Therefore, the total value of the raffle is equal to: $1400 + ($5 × 833) = $1400 + $4165 = $5565
The expected value of a ticket is the total value of the raffle divided by the number of tickets sold.
Therefore, the expected value of a ticket is:$5565 / 833 = $6.68
Therefore, the expected value (the mean of the distribution) for someone who buys a ticket is $6.68.
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Chang needs to drive 11 miles to work. So far, he has driven 4.7 miles. How many more miles must he drive?
Answers
Answer:
6.3 miles
Step-by-step explanation:
11-4.7 = 6.3 hope this helps
He requires to travel 6.3 miles more to reach work.
Distance is the measure of how far apart two points are. It is a scalar quantity that is typically measured in units such as meters, kilometers, miles, feet, or inches.
Since the total distance required to be traveled by Chang is 11 miles.
Let S = total distance = 11
given distance traveled is 4.7 miles
take this traveled distance of 4.7 miles as x
now let S = x+y
replacing the given values where S = 11, x = 4.7
11= 4.7+y
y=11-4.7
y= 6.3
hence the remaining distance required to be traveled by Chang is 6.3 miles.
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the weights of steers in a herd are distributed normally. the standard deviation is 300lbs and the mean steer weight is 1100lbs . find the probability that the weight of a randomly selected steer is between 1279 and 1609lbs
Answers
The probability that the weight of a randomly selected steer is between 1279 and 1609 lbs is 0.2288.
Given that the weights of steers in a herd are distributed normally.
The standard deviation is 300 lbs and the mean steer weight is 1100 lbs.
We are required to find the probability that the weight of a randomly selected steer is between 1279 and 1609 lbs.
Here, it is given that the mean weight of the herd is 1100 lbs and the standard deviation is 300 lbs.
We need to find the probability of the weight of a randomly selected steer between 1279 lbs and 1609 lbs.
It can be written as;
P (1279 ≤ X ≤ 1609)
We can standardize this distribution by subtracting the mean and dividing it by the standard deviation.
The standardized form is given by
Z = (X-μ)/σ
where X is the given value, μ is the mean and σ is the standard deviation.
Substituting the values we get,
for X = 1279
[tex]Z_1[/tex] = (1279 - 1100)/300 = 0.5967 and
for X = 1609
[tex]Z_2[/tex] = (1609 - 1100)/300 = 1.6967
We are required to find the probability of Z between [tex]Z_1[/tex] and [tex]Z_2[/tex].
P([tex]Z_1[/tex] ≤ Z ≤ [tex]Z_2[/tex]) To find this probability,
we use the standard normal distribution table,
We get P(Z ≤ 1.70) = 0.9545 and P(Z ≤ 0.60) = 0.7257
Now, P ([tex]Z_1[/tex] ≤ Z ≤ [tex]Z_2[/tex]) = P(Z ≤ 1.70) - P(Z ≤ 0.60) = 0.9545 - 0.7257 = 0.2288.
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15 - (p + 1) where p = 3 and 4 = 10 calculate
Answers
Answer:
11
Step-by-step explanation:
15 - (p + 1)
Let p=3
15 - (3 + 1)
Parentheses first
15 - (4)
11
Answer:
11
Step-by-step explanation:
Given that,
p = 3
So, to find the value of the expression you have to solve it by replacing p with 3.
15 - ( p + 1 )
15 - ( 3 + 1 )
15 - 4
11
26. In the given figure, OP || RS. ZPQR = 60° and QRS = 130°. Then what is the measure of ZOPQ? S P 60% R 130⁰
Answers
Answer: The answer is 60.
Step-by-step explanation:
Using the fact that OP || RS, we know that∠RWV = 180° − 130° 1. ∠RWV = 50° We know that,∠PWQ = ∠RWV = 50° (Since, opposite angles of intersecting lines are equal) Also, for line OP∠OQP + θ = 180° θ = 180° − ∠OPQ = 180° − 110° 2. θ = 70°
Answer:
The measure of ∠OPQ is 110°.
Step-by-step explanation:
Draw a line parallel to OP from point Q. Label a point on the line T. (See attached diagram).
Angles SRQ and TQR are alternate interior angles, and so according to the Alternate Interior Angles Theorem, they are congruent.
⇒ m∠TQR = m∠SRQ = 130°
Given m∠PQR = 60° and m∠TQR = 130° then:
⇒ m∠TQP + m∠PQR = m∠TQR
⇒ m∠TQP + 60° = 130°
⇒ m∠TQP = 70°
Angles OPQ and TQP are same-side interior angles, and so according to the Same-side Interior Angles Theorem, they are supplementary (sum to 180°).
⇒ m∠OPQ + m∠TQP = 180°
⇒ m∠OPQ + 70° = 180°
⇒ m∠OPQ = 110°
Therefore, the measure of ∠OPQ is 110°.
What is the percent of wolves that are neither female nor hunt in medium‑sized packs?
Answers
Number of wolves hunting in medium-sized packs) to perform these calculations and obtain the percentage.
To find the percent of wolves that are neither female nor hunt in medium-sized packs, follow these steps:
1. Determine the total number of wolves.
2. Identify the number of female wolves and those that hunt in medium-sized packs.
3. Subtract the number of wolves that fit into either category from the total number of wolves.
4. Divide the remaining number of wolves by the total number and multiply by 100 to get the percentage.
Please provide the necessary data (total number of wolves, number of female wolves, and number of wolves hunting in medium-sized packs) to perform these calculations and obtain the percentage.
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The triangles are similar. Find the value of x.
Answers
Since the triangles are similar, the value of x is equal to: C. 18 units.
What are the properties of similar triangles?In Mathematics, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
By applying the properties of similar triangles, we have the following ratio of corresponding side lengths;
AC/RS = AB/RT
By substituting the given side lengths into the above equation, we have the following:
x/24 = 24/32
By cross-multiplying, we have the following;
32x = 24(24)
32x = 576
x = 576/32
x = 18 units.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
architects often create scale models before the actual building is constructed. if a scale model has a length of 24 inches and a width of 36 in., which dimensions are geometrically similar to the model buildings?
Answers
Architects often create scale models before the actual building is constructed. if a scale model has a length of 24 inches and a width of 36 in., 2:3 the dimensions are geometrically similar to the model buildings
Geometrically similar to the model buildings are those whose ratio of corresponding dimensions are the same as those of the model.
The ratio of the dimensions of the scale model is:
length:width = 24:36 = 2:3
There are two ratios to compare in a building with dimensions L and W:
length : width = L:W and
width : length = W:L
The ratio of the dimensions of a building must be in proportion to the ratio of the dimensions of the scale model for geometric similarity.
Since the dimensions of the model are 2:3, the dimensions of the building must also be in a 2:3 ratio.
Therefore, we have: L : W = 2:3
L = (2/3)W
The ratio of the length to the width of the building is 2:3.
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the sum of two rational numbers is 85. if one number is 5 more than the other, then what are the numbers?
Answers
Answer:
40 and 45
Step-by-step explanation:
let the 2 numbers be x and y with y the larger of the two, then
x + y = 85 → (1)
x = y + 5 → (2)
substitute x = y + 5 into (1)
y + 5 + y = 85
2y + 5 = 85 ( subtract 5 from both sides )
2y = 80 ( divide both sides by 2 )
y = 40
substitute y = 40 into (2)
x = 40 + 5 = 45
the two numbers are 40 and 45
the 98.4% confidence interval for snapdragons grown in compost is (20.91, 38.43). what is the margin of error of this confidence interval?
Answers
The margin of error of the 98.4% confidence interval for snapdragons is 3.71.
The midpoint of the range is calculated by adding the upper and lower bounds and then dividing by two. So, the sample mean is `(20.91 + 38.43) / 2 = 29.67`.
The margin of error is calculated by multiplying the critical value of z* (1.96 for a 98.4% confidence level) by the standard error of the mean. The formula for calculating the margin of error is:
`Margin of error z*(standard deviation/√n`).
The formula is `range/4 = 1.96 * standard deviation/√n`.Now, solve for the standard deviation:
`standard deviation = (range/4) * √n / 1.96`
Substituting the values: `(38.43 - 20.91)/4 = 1.96 * standard deviation/√n`
Simplifying the equation: `4.26 = (1.96*standard deviation)/√n`
Squaring both sides: `4.26^2 = 3.8416 = (1.96^2 * standard deviation^2)/n`
Substituting the value of the standard deviation: `3.8416 = (1.96^2 * ((38.43 - 20.91)/4)^2) / n`
Solving for n: `n = ((1.96^2 * ((38.43 - 20.91)/4)^2) / 3.8416) = 31.54`
Now that we know the sample size, we can calculate the standard error of the mean:
`standard error = standard deviation/√n = ((38.43 - 20.91)/4)/√31.54 = 1.89`.
The margin of error is `1.96 * 1.89 = 3.71`.
The 98.4% confidence interval for snapdragons grown in compost is (20.91, 38.43). The margin of error of this confidence interval is 3.71.
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christina's pizza sells pizza by the slice for lunch. today, they sold 76 slices, including 20 slices of pepperoni pizza. what is the experimental probability that the first slice sold during lunch tomorrow will be a slice of pepperoni pizza?
Answers
The experimental probability that the first slice sold during lunch tomorrow will be a slice of pepperoni pizza is approximately 0.263
The experimental probability is found by dividing the number of times the desired outcome occurred by the total number of trials. In this case, the desired outcome is selling a slice of pepperoni pizza as the first slice tomorrow.
Since we only know the number of slices sold today, we don't have any specific information about the number of slices that will be sold tomorrow. However, we can assume that the same types of pizzas will be sold tomorrow, and the probability of selling a slice of pepperoni pizza tomorrow will be the same as the proportion of pepperoni slices sold today.
So, the experimental probability that the first slice sold during lunch tomorrow will be a slice of pepperoni pizza is
Experimental probability = Number of pepperoni slices sold today / Total number of slices sold today
Experimental probability = 20 / 76
Experimental probability = 0.263
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Seth is analyzing the number of students in his class and
Answers
The least likely event from given events is Option B: A randomly selected student who is freshmen owns a skateboard.
The event whose occurence is minimum is least likely event.
Suppose there are finite elementary events in sample space of considered experiment and all are equally likely.
Then, we want to find the probability of an event E.
Then, its probability is given as
P(E) = Number of favourable cases/ Number of total cases = n(E)/n(S)
where favorable cases are the elementary events who belong to E, and total cases are size of sample space.
For two events A and B, by chain rule, we have:
P(A∩B) = P(B)P(A|B) = P(A)P(A|B)
How to find the conditional probability:
Suppose that there are two events A and B. Then suppose the conditional probability are:
P(A|B) = probability of occurrence of A given B has already occurred.
P(B|A) = probability of occurrence of B given A has already occurred.
We can then use the chain rule to find them, or Bayes theorem also helps in finding these probabilities.
We are given the table of joint relative frequency:
We take events as A, A' and B and B'
Important probabilities which will be used are evaluated as:
P(A) = n(A)/n(S) = 150/1200 = 1/8
P(B) = n(B)/n(S) = 250/1200 = 5/24
P(A') = 1 - P(A) = 7/8
P(B') = 1 - P(B) = 1 - 5/24 = 19/24
P(A∩B) = n(A∩B) / n(S) = 40/1200 = 1/30
P(A'∩B') = n(A'∩B') / n(S) = 840/1200 = 7/10
P(A'∩B) = n(A'∩B) / n(S) = 210/1200 = 7/40
Evaluating probabilities of choices given, we get:
Case 1: E = A random selected student who owns skateboard is freshmen
P(E) = ?
P(E) = P(B|A) = P(A∩B) / P(A) = 1/30 ÷ 1/8 = 4/15
Case 2: E = A random selected student who is freshmen owns skateboard:
P(E) = P(A|B) = P(A∩B) / P(B) = 1/30 ÷ 5/24 = 4/25
Case 3: E = A random selected student who doesn't owns skateboard is freshmen
P(E) = P(B|A') = P(A'∩B) / P(A') = 7/40 ÷ 19/24 = 21/95
Case 4: E = A randomly selected student who doesn't owns skateboard is not freshmen
P(E) = P(B'|A') = P(A'∩B') / P(A') = 7/10 ÷ 19/24 = 84/95
So, the least probability is for second case.
Question - Seth is analyzing number of students in class and high school who own skateboards. He puts the data in table shown. Given information in table, which event is least likely?
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The sine is negative between 180 and 360 degrees true or false
Answers
Answer:
true
Step-by-step explanation:
3rd quadrant sine is (-)
4th quadrant sine is (-)
siona bought 10 outfits to wear to church. the shirt has a price of $3.50 and a pair of shorts has a price of $4.00. how many shirts and pairs of shorts did she buy when she spent a total of $36.50?
Answers
Siona bought 7 shirts and 3 pairs of shorts when she spent a total of $36.50. The problem can be solved using a system of equations.
Let's use a system of equations to solve this problem:
Let x be the number of shirts that Siona bought, and y be the number of pairs of shorts that she bought. Then we have:
Equation 1: x + y = 10 (Siona bought 10 outfits in total)
Equation 2: 3.50x + 4.00y = 36.50 (The total cost of the outfits is $36.50)
To solve for x and y, we can use substitution or elimination. Let's use substitution:
From Equation 1, we can solve for x in terms of y:
x = 10 - y
Substitute this expression for x into Equation 2:
3.50(10 - y) + 4.00y = 36.50
Simplify and solve for y:
35 - 3.50y + 4.00y = 36.50
0.50y = 1.50
y = 3
Now we can substitute y = 3 back into Equation 1 to solve for x:
x + 3 = 10
x = 7
Therefore, Siona bought 7 shirts and 3 pairs of shorts when she spent a total of $36.50.
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3.- cual es la máxima distancia que pueden recorrer sin cambiar de dirección en una pista de patinaje en forma de rombo, si cada lado mide 26 mts y ka diagonal menor 40 mts ?
Answers
Consequently, in this rhombus-shaped skating rink, the longest distance that may be covered without changing directions is 40 metres.
what is perimeter ?The total distance encircling a two-dimensional shape's perimeter is known as its perimeter. It represents the total length of the shape's sides. The perimeter of a rectangle, for instance, can be determined by combining the lengths of its four sides: A rectangle's perimeter equals 2 x (length + width). Other shapes, such triangles, circles, and polygons, can have their perimeters determined using the appropriate formulas.
given
The formula for the perimeter of a rhombus, which is the sum of the lengths of its four sides, can be used to determine the greatest distance that can be covered in a rhombus-shaped skating rink without changing direction.
Given that the sides are each 26 metres long, the rhombus's perimeter would be:
Perimeter: (4 x 26) = 104 metres
But, we must consider that the smaller diagonal of the skating rink measures 40 metres in order to determine the most distance that may be traversed without changing directions. This means that the skater is limited to a 40-meter radius before having to change directions.
Consequently, in this rhombus-shaped skating rink, the longest distance that may be covered without changing directions is 40 metres.
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The complete question is:- 3.- What is the maximum distance that can be traveled without changing direction in a rhombus-shaped skating rink, if each side measures 26 meters and the smaller diagonal is 40 meters?
Solve Systems of Equations
Y= 1/2x
3y= x-1
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Mary bought 8 blouses and 3 skirts for a total of $120.00. Kristy bought 5 blouses and 5 skirts at the same prices for a total of $112.50. What is the cost of each blouse and each skirt?
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After solving the equations we know that the price of each blouse and each skirt is $25 and $30 respectively.
What are equations?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation.
As in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others.
The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.
So, the cost of each blouse and skirt:
x be the price of one blouse and y is the price of one skirt.
For a total of $215, Carol purchased 3 skirts and 5 blouses.
5x + 3y = 215
For a total of $135, Ellen purchased 2 skirts and 3 blouses.
3x + 2y = 135
By resolving the equations in the system:
5x + 3y = 215
3x + 2y = 135
We will obtain:
x = $25
y = $30
Therefore, after solving the equations we know that the price of each blouse and each skirt is $25 and $30 respectively.
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Correct question:
Carol bought 5 blouses and 3 skirts for a total of $215. At the same time, her sister Ellen bought 3 blouses and 2 skirts for a total of $135. What was the price of each blouse and each skirt?
find n 3ft area=33 sq ft
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The dimensions of the rectangle are 6 ft by 5.5 ft, and n = 6.
What is the area of the rectangle?
To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.
We know that the area of a rectangle is given by:
Area = Length x Width
Since the problem does not specify the shape of the rectangle, we cannot assume that it is a square. Therefore, we need to find two numbers whose product is 33.
The factors of 33 are 1, 3, 11, and 33. None of these factors is equal to 3, so we cannot simply multiply 3 by a factor of 33 to get the length of the rectangle. Therefore, we need to use a different approach.
One way to find two numbers whose product is 33 is to start with the square root of 33 and round up and down to the nearest integer. The two resulting integers will be close to the factors of 33 and will multiply to give 33.
The square root of 33 is approximately 5.74. Rounding up and down to the nearest integer gives:
Length = 6 ft
Width = 33 ÷ 6 = 5.5 ft (approximately)
The product of these two numbers is:
6 ft x 5.5 ft ≈ 33 sq ft
Therefore, the dimensions of the rectangle are 6 ft by 5.5 ft, and n = 6.
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