The actual distance between the two cities is 432 miles.
The figure shows a map of two cities, with a distance between them measured at 4.5 inches.
The scale of the map is given as 1/8 inch to 12 miles.
This means that 1/8 inch on the map represents a distance of 12 miles in real life.
To determine the actual distance between the two cities, we can use the scale provided.
1/8 inch on the map represents 12 miles in real life.
A proportion to find the actual distance between the cities:
1/8 inch on map = 12 miles in real life
4.5 inches on map = x miles in real life
To solve for x, we can cross-multiply and simplify:
1/8 × x = 12 × 4.5
x = 12 × 4.5 × 8
x = 432 miles
Maps with scales can be useful for determining distances, sizes, and proportions of objects in real life.
It allows us to visually represent complex spatial relationships and make measurements without physically being present at the location.
Remember to use the correct scale and make sure to convert units properly in order to accurately determine real-life measurements.
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Which factor of 24 can help you solve 24 divided by 4?
Answer:
im an expert
Step-by-step explanation:
Round 73,609 to the nearest thousand
Answer:
74,000
Step-by-step explanation:
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help me please!! I’m not quite sure how to solve this so explanations for this will be appreciated
The solution is:
the area of this figure is 21.9 ft².
Here, we have,
To find the area of this figure, we must find the area of the 6 x 6 square and subtract the area of a semi-circle with a diameter of 6.
Area square:
6 x 6
36
Area semi-circe:
A = 1/2(πr²)
A = 1/2(6/2)²π
A = 1/2(9π)
A = 14.1
Area shape:
36 - 14.1
21.9
The units are ft², so the answer is 21.9 ft².
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Gavin is working two summer jobs making $14 per hour tutoring and $13 per hour landscaping. Last week Gavin worked a total of 10 hours and earned a total of $137. Determine the number of hours Gavin worked tutoring last week and the number of hours he worked landscaping last week.
Answer:
3 landscaping, 3 tutoring
Step-by-step explanation:
This is a system of equations.
Let T = number hours tutoring and L = number hours landscaping.
T + L = 10
137 = 14T + 13L
Now solve the system of equations.
We can rearrange the first equation so that T = 10-L. Substitute that in the 2nd equation.
137=14(10-L) + 13L
137 = 140-14L + 13L
-3=-L
3=L
He worked 3 Landscaping Hours. Substitute back into the original equation to solve for T (tutoring hours).
T+L = 10
T+3 = 10
T = 7.
We worked 7 tutoring hours.
Now double check with the earnings equation.
137 = 14T + 13L
137 = 14*7+ 13*3
137 = 98 + 39
137=137
A study of religious practices among college students interviewed a sample of 125
students; 105
of the students said that they prayed at least once in a while. What is the sample proportion who said they pray?
0.84
1.19
105
84
The sample proportion who said they pray is approximately 0.84, or 84%.
How to solve for the sample proportionThe sample proportion of college students who said they pray can be calculated by dividing the number of students who said they pray (105) by the total number of students in the sample (125).
Sample proportion = Number of students who said they pray / Total number of students in the sample
Sample proportion = 105 / 125
Sample proportion = 0.84
Therefore, the sample proportion who said they pray is approximately 0.84, or 84%.
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1459 divided by 6 with remainder as fraction
Answer:
6 1/243
Step-by-step explanation:
6 goes into 1459, 243 times
243*6=1458
1459-1458=1
So there is a remainder of 1
So the answer would be 6 1/243
How does Mathematics differ from language to language across the world
The answer is explained below.
In order to be considered a language, a system of communication must have vocabulary, grammar, syntax, and people who use and understand it. Mathematics meets this definition of a language. Linguists who don't consider math a language cite its use as a written rather than spoken form of communication.
Mathematics is pure language - the language of science. It is unique among languages in its ability to provide precise expression for every thought or concept that can be formulated in its terms. In a spoken language, there exist words, like "happiness", that defy definition.
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513.4497 rounded to the hundredths place
Answer:
513.45
Step-by-step explanation:
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Out of 1000 students who appeared in an examination,60% passed the examination.60% of the failing students failed in mathematics and 50% of the failing students failed in English.If the students failed in English and Mathematics only, find the number of students who failed in both subjects.
The value of number of students who failed in both mathematics and English is 40.
Since, Given that;
60% of the 1000 students passed the examination,
Hence, we can calculate the number of students who passed the exam as follows:
60/100 x 1000 = 600
So, 600 students passed the examination.
Now, let's find the number of students who failed the examination.
Since 60% of the students passed, the remaining 40% must have failed. Therefore, the number of students who failed the examination is:
40/100 x 1000 = 400
Of the 400 failing students, we know that 60% failed in mathematics.
So, the number of students who failed in mathematics is:
60/100 x 400 = 240
Similarly, we know that 50% of the failing students failed in English.
So, the number of students who failed in English is:
50/100 x 400 = 200
Now, we need to find the number of students who failed in both subjects.
We can use the formula:
Total = A + B - Both
Where A is the number of students who failed in mathematics, B is the number of students who failed in English, and Both is the number of students who failed in both subjects.
Substituting the values we have, we get:
400 = 240 + 200 - Both
Solving for Both, we get:
Both = 240 + 200 - 400
Both = 40
Therefore, the number of students who failed in both mathematics and English is 40.
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The dosage the pharmacy carries in stock (on hand), is different than the prescribers order. Use ratio and proportion to calculate the total quantity of tablets to dispense for each of the prescriptions below: Order: Zocor 40 mg po qd for 60 days On hand: 20 mg tabs How many 20 mg tabs should be given? Give:
Using ratios and proportions, the number of 20 mg tabs that should be given in place of 40 mg po qd for 60 days is 120 tabs.
How the number is determined:Using ratios and proportions, the number of tabs of 20 mg that should be given in place of 40 mg qd for 60 days is determined as follows:
Order: Zocor 40 mg po qd for 60 days
= 60 tabs since it is once per day (qd)
Total mg = 2,400 mg (40 mg x 60 tabs)
On hand: 20 mg tabs
Proportionately, 20 mg = 120 tabs (2 x 60) since 40 mg is for 60 tabs
Total mg = 2,400 mg (20 mg x 120 tabs)
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Scores on a final exam in a large class were normally distributed with a mean of 75 and a standard deviation of 8. What percent of the students scored above an 83?
Using z - score, the percentage of students above 83 is 15.9%
What is the percentage of students that scored above 83?To find the number of students that scored above 83 can be calculated using z - score formula.
This is given as
z = x - μ / σ
μ = meanσ = standard deviationx = scoreSubstituting the values into the formula;
z = 83 - 75 / 8
z = 1
The z-score is 1
Let's find the percentage of z -score under the score
p(x > 83) = 1 - P(x < 83) = 0.15866
p = 15.9%
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A golf ball rolls at a speed of 8 m/s for 12 seconds. Mandy hits the golf ball and it rolls
for 16 seconds at a speed of 12 m/s. What is the total distance travelled by the golf ball?
Using the given information, the total distance travelled by the golf ball is 288 m
Calculating the total distance travelled by the golf ballFrom the question, we are to calculate the total distance travelled by the golf ball
The distance travelled by the golf ball can be calculated by using the formula,
Distance = Speed × Time
From the given information,
The golf ball rolls at a speed of 8 m/s for 12 seconds
Thus,
The distance travelled at this time is
Distance = 8 m/s × 12 s
Distance = 96 m
Also,
Mandy hits the golf ball and it rolls for 16 seconds at a speed of 12 m/s
The distance travelled at this time is
Distance = 12 m/s × 16 s
Distance = 192 m
The total distance travelled by the golf ball is 96 m + 192 m
=
Hence, the total distance travelled by the golf ball is 288 m
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URGENT HELP PLEASE!!!
In a class of students, the following data table summarizes how many students have a
a
cat or a dog. What is the probability that a student chosen randomly from the class
has a cat and a dog?
Answer: 5/13
Step-by-step explanation:
To solve this problem, we can use the formula for conditional probability:
P(A|B) = P(A and B) / P(B)
where P(A and B) is the probability of both events A and B happening, and P(B) is the probability of event B happening.
Let's first calculate the total number of people in the class:
Total number of people = 5 + 6 + 2 + 11 = 24
Now, let's calculate the probability of having a cat and a dog:
P(cat and dog) = 5 / 24
Next, let's calculate the probability of having a cat:
P(cat) = (5 + 6 + 2) / 24 = 13 / 24
Finally, let's calculate the probability of having no dog:
P(no dog) = (6 + 11) / 24 = 17 / 24
Using the formula for conditional probability, we can calculate the probability of having both a cat and a dog given that a person has a cat:
P(cat and dog | cat) = P(cat and dog) / P(cat) = (5 / 24) / (13 / 24) = 5 / 13
Therefore, the probability that a student chosen randomly from the class has a cat and a dog is 5/13.