Final answer:
The speed of the slower plane is 425 mph, and the speed of the faster plane is 460 mph, determined by using the concept of relative speed and algebra to solve the given equation.
Explanation:
To solve the problem of two planes flying towards each other, we need to use the concept of relative speed. We know that the two planes are 3540 miles apart and that they pass each other after 4 hours. The speeds of the planes differ by 35 mph. The relative speed of the two planes combined is the distance divided by the time, so we calculate it as follows:
Relative Speed = Total Distance / Time = 3540 miles / 4 hours = 885 mph
So, if we denote the speed of the slower plane as S mph, the speed of the faster plane will be S + 35 mph. Since their combined speed is the relative speed, we can set up the following equation:
S + (S + 35) = 885
From this equation, we need to find the value of S which represents the speed of the slower plane. We can then add 35 to S to find the speed of the faster plane. Here's how it's done step by step:
Combine like terms: 2S + 35 = 885Subtract 35 from both sides: 2S = 850Divide by 2 to solve for S: S = 425 mphAdd 35 to S to find the speed of the faster plane: 425 + 35 = 460 mphTherefore, the speed of the slower plane is 425 mph and the speed of the faster plane is 460 mph.
there are 207 students in 9 classes at east middle school at this rate how many students are in six classes
Which fraction shows 2.8 as the quotient of two integers?
14/5
12/5
9/4
9/2
Answer:14/5 is the correct answer, just took test
Step-by-step explanation:
In Ms. Hendricks class, there are 10 boys and 12 girls. What is the ratio of boys to girls? Express your answer as a fraction in simplest form.
logan made a treasure hunt map.the treasure is 25cm away from his location.if each 1cm on the scale drawing equals 5 meters, then how far he is from treasure?
Logan's treasure is represented as 25 cm away on his map; using the scale of 1 cm to 5 meters, it can be calculated that he is 125 meters away from the treasure by multiplying the map distance by the scale factor.
Logan has created a treasure hunt map where the scale indicates that 1 cm on the map corresponds to an actual distance of 5 meters. To determine the actual distance Logan is from the treasure, we first note that the treasure is shown as 25 cm away from his location on the map. Since the scale factor is 1 cm to 5 meters, we can set up a simple multiplication to find the actual distance.
The calculation would be as follows:
Scale factor: 1 cm = 5 meters
Map distance: 25 cm
Actual distance: 25 cm x 5 meters/cm
By multiplying the map distance by the scale factor, we get:
Actual distance = 25 x 5 = 125 meters
Therefore, Logan is 125 meters away from the treasure.
Two of the sides of an isosceles triangle have lengths of 10 cm and 4 cm. what is the length of the base?
An isosceles triangle is a triangle that has any two sides equal in length and angles opposite to equal sides are equal in measure.
The unequal side is the base of the triangle.
The length of the base of the isosceles triangle is
10 cm or 4 cm.
What is an isosceles triangle?An isosceles triangle is a triangle that has any two sides equal in length and angles opposite to equal sides are equal in measure.
The unequal side is the base of the triangle.
We have,
Two sides of an isosceles triangle have lengths:
= 10 cm and 4 cm
The unequal side of the isosceles triangle is the base and the other two sides have to be equal.
We can have two cases-
Case 1.
If the equal two sides are 10 cm.
Base = 4 cm
Case 2.
If the equal two sides are 4 cm.
Base = 10 cm.
Thus the length of the base of the isosceles triangle is
10 cm or 4 cm.
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Jeremy is shopping online for skating equipment. He buys a longboard complete with trucks and wheels for $146.25. At checkout, Jeremy gets a discount of $21 on his purchase. The final amount that Jeremy will be billed is $ 42.00 104.25 125.25 167.25
Answer:
Option C. $125.25
Step-by-step explanation:
Jeremy is shopping online for skating equipment.
The price of long board with trucks and wheels = $146.25
Jeremy gets a discount on his purchase = $21.00
the final amount that Jeremy would be billed.
We subtract the discount from the price of item.
= $146.25 - $21.00 = $125.25
The final amount that Jeremy would be billed is $125.25.
What is the effective rate on a $10,000 treasury bill 4% for 13 weeks?
Final answer:
The effective rate on a $10,000 treasury bill with a nominal rate of 4% for 13 weeks is 4.06%.
Explanation:
The effective rate on a treasury bill is the annualized interest rate that takes into account the compounding of interest over the term of the bill. To calculate the effective rate, you can use the formula:
[tex]Effective Rate = (1 + (Nominal Rate / M))^M - 1[/tex]
Where:
Effective Rate is the annualized interest rateNominal Rate is the stated interest rate (4% in this case)M is the number of compounding periods in one year (for a treasury bill, usually 4 as it is a 13-week bill)Plugging in the values:
Effective Rate = [tex](1 + (0.04 / 4))^4[/tex]- 1
= [tex](1 + 0.01)^4 - 1[/tex]
= [tex]1.01^4 - 1[/tex]
= 1.04060401 - 1
= 0.04060401 (or 4.06% rounded to two decimal places)
Therefore, the effective rate on a $10,000 treasury bill with a nominal rate of 4% for 13 weeks is 4.06%.
The Graduate Management Admission Test (GMAT) is a standardized exam used by many universities as part of the assessment for admission to graduate study in business. The average GMAT score is 547 (Magoosh website, January 5, 2015). Assume that GMAT scores are bell-shaped with a standard deviation of 100.
. What percentage of GMAT scores are 647 or higher?
15.8
b. What percentage of GMAT scores are 747 or higher (to 1 decimal)?
2.9
c. What percentage of GMAT scores are between 447 and 547 ?
25
d. What percentage of GMAT scores are between 347 and 647 (to 1 decimal)?
Answer:
16%; 2.5%; 34%; 81.5%
Step-by-step explanation:
Using the empirical rule, we know that 68% of data falls within one standard deviation of the mean; 95% of data falls within two standard deviations of the mean; and 99.7% of data falls within 3 standard deviations of the mean.
This means from the mean to 1 standard deviation (σ) above is 34% of data; from the mean to 1 σ below is 34% of data; from 1 σ to 2σ above is 13.5% of data; from 1σ to 2σ below is 13.5% of data; from 2σ to 3σ above is 2.35% of data; from 2σ to 3σ below is 2.35% of data; more than 3σ above is 0.15% of data; and more than 3σ below is 0.15% of data.
647 is 1 σ above the mean. This means that we go from here above;
13.5+2.35+0.15 = 16%
747 is 2σ above the mean. This means that we go from here above:
2.35+0.15 = 2.5%
447 is 1σ below the mean and 547 is the mean. This means that we have 34%.
347 is 2σ below the mean and 647 is 1 above the mean. This means we go from:
13.5+34+34 = 81.5%
To find the percentage of GMAT scores between 347 and 647, find the z-scores and use a z-table to calculate the cumulative area.
Explanation:To find the percentage of GMAT scores between 347 and 647, we need to find the area under the bell curve between these two scores. First, we need to find the z-scores for both scores using the formula z = (x - μ) / σ. For 347, the z-score is (-200) / 100 = -2, and for 647, the z-score is 100 / 100 = 1.
Next, we need to find the percentage of data between these z-scores. We can use a z-table to find the cumulative area. The cumulative area for -2 is 0.0228 and for 1 is 0.8413.
To find the percentage between these two z-scores, we subtract the cumulative area for -2 from the cumulative area for 1: 0.8413 - 0.0228 = 0.8185.
Therefore, the percentage of GMAT scores between 347 and 647 is 81.85%.
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Solve x2 – 8x = 20 by completing the square. Which is the solution set of the equation? {–22, 14} {–14, 22} {–10, 2} {–2, 10}
Answer: D is the right answer. The solution set of the given equation={-2,10}.
Explanation:
Given equation: [tex]x^2-8x=20[/tex]
The standard perfect square trinomial equation is [tex]x^2+2ax+a^2=(x+a)^2[/tex]
On comparing this with the left side of the given equation ,we get 2a=-8
⇒a= -4 and [tex]a^2=16[/tex]
Now to make given equation perfect square add 16 on the both sides, we get [tex]x^2-8x+16=20+16\\\Rightarrow(x-4)^2=36[/tex]
Taking square root on both the sides we get,
[tex]x-4=-6\ or\ x-4=6[/tex]
add 4 on both sides, we get
⇒x= -6+4 or x=6+4
⇒x=-2 or x=10
Therefore, the solution set of the given equation={-2,10}.
Thus D is the right answer.
A) what value represents the 40th percentile of these returns?
f(x)=x g(x)=1 what is the domain of (g/f)(x)
[tex]\left(\dfrac{g}{f}\right)(x)=\dfrac{g(x)}{f(x)}\\\\\text{We have}\ f(x)=x\ \text{and}\ g(x)=1.\ \text{Substitute}\\\\\left(\dfrac{g}{f}\right)(x)=\dfrac{1}{x}\\\\\text{The domain}:\ x\neq0\\\\Answer:\ \boxed{\text{All real numbers except 0}\to x\in\mathbb{R}-\{0\}}[/tex]
The domain of the function is a real number except 0 because the function is not defined at x = 0.
What are domain and range?The domain means all the possible values of x and the range means all the possible values of y.
The functions are given below.
f(x) = x
g(x) = 1
Then the domain of the function (g/f)(x) will be
(g/f)(x) = 1 / x
Then the graph of the function is given below.
The domain of the function is a real number except 0 because the function is not defined at x = 0.
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TIMMY and JEROD are eating cupcakes if they each can eat 2 cupcakes in 3 minutes how long will it take them to eat 18 cupcakes?
Jean-Marc used a scale factor of 5 to make this scale drawing of a moth.
In the drawing, the wingspan of the moth measures 3 centimeters. What was the actual wingspan, in millimeters, of the moth Jean-Marc observed?
A rectangle is drawn so that the width is 2 feet shorter than the length. The area of the rectangle is 80 square feet. Find the length of the rectangle.
Final answer:
To find the length of the rectangle, set up a proportion using the given information. Solve the equation to find the length of the rectangle is 10 feet.
Explanation:
To find the length of the rectangle, we can set up a proportion using the given information. Let the length of the rectangle be L and the width be W. From the problem, we know that the width is 2 feet shorter than the length, so we can write the equation W = L - 2. We also know that the area of the rectangle is 80 square feet, so we can write the equation L * W = 80.
Substituting W = L - 2 into the equation L * W = 80, we get L * (L - 2) = 80. Expanding and rearranging the equation gives us L2 - 2L - 80 = 0. Factoring the quadratic equation, we find (L - 10)(L + 8) = 0.
Since we are looking for the length of the rectangle, we discard the negative solution and find that L = 10. Therefore, the length of the rectangle is 10 feet.
A package of 10 cans of soup costs $14. An individual can costs $2. You need at least 25 cans. Find You decide to buy 3 packages of 10 cans. How much do you pay for each can?the price of each combination of items.You decide to buy 3 packages of 10 cans. How much do you pay for each can?
To find the cost per can when buying 3 packages of cans, multiply the cost of a single package by 3 to get the total cost, then divide the total cost by the total number of cans to find the cost per can.
To find the cost per can when buying 3 packages of 10 cans each:
Cost of 1 package with 10 cans = $14Cost of 3 packages = 3 x $14 = $42Number of cans = 3 packages x 10 cans per package = 30 cansCost per can = Total cost / Number of cans = $42 / 30 cans = $1.40According to the Journal of the American Medical Association (JAMA), hospitals that routinely staff with 1:8 nurse-to-patient ratios experience five additional deaths per 1,000 patients than those staffing with 1:4 ratios (2002). If the local hospital has decided to follow the 1:4 nurse-to-patient ratio, how many patients can they treat if they have 120 nurses?
Final answer:
The local hospital can treat a maximum of 480 patients if they follow the 1:4 nurse-to-patient ratio and have 120 nurses.
Explanation:
The local hospital can treat a maximum of 480 patients if they follow the 1:4 nurse-to-patient ratio and have 120 nurses.
To calculate the maximum number of patients the hospital can treat, we divide the number of nurses by the nurse-to-patient ratio. In this case, the ratio is 1:4, so for every 1 nurse, there are 4 patients. Therefore, each nurse can handle 4 patients.
To find the maximum number of patients, we multiply the number of nurses by the number of patients each nurse can handle. In this case, 120 nurses multiplied by 4 patients per nurse equals 480 patients.
Pedro deposited $35 then withdrew $50 show number line graph
NEED HELP !!!!!
put a check mark for the correct term (rational irrational )
61 pie
42
75.671523
101
6/5
Solve: 3x - 2x + 4 = 5x - 4x - 8
In Zoe's class, 4 /5 of the students have pets. Of the students who have pets, 1/8 have rodents. What fraction of the students in Zoe's class have rodents? Enter the answer in simplest form. The fraction of students in Zoe's class who have rodents is
Answer:
The fraction of students in Zoe's class who have rodents is [tex]\frac{1}{10}[/tex].
Step-by-step explanation:
In Zoe's class, 4 /5 of the students have pets.
Of the students who have pets, 1/8 have rodents.
This means [tex]\frac{1}{8} of \frac{4}{5}[/tex] have rodents.
So,fraction of students who have rodents = [tex]\frac{1}{8}\times\frac{4}{5}[/tex]
= [tex]\frac{1}{10}[/tex]
The fraction of students in Zoe's class who have rodents is [tex]\frac{1}{10}[/tex].
Miki has a sheet of paper with a length of 104 centimeters and a width of 88 centimeters. She wants to divide it into the largest squares possible without wasting any paper. How many squares of the largest size will she be able to cut from the paper? 13 squares, 26 squares, 143 squares, or 572 squares
600,000 to the nearest hundred thousand is
How to find the general solution to y"'+2y"-4y'-8y=0?
Qual é a diferença entre a população de Toledo e Umuarama?
Toledo - 119 207
Umuarama - 100 716
350 kilometers in 5 hours in unit rate
Answer:
70 kilometers per hour.
Step-by-step explanation:
Remember that unit rate is the direct correlation between two different units, but the numerator should be 1, this means that for example if you can cook 20 muffins in 4 ovens, you have to calculate how many muffins can you cook in one oven, to calculate this problem you have to divide the kilometers by the hours you have:
350 kilometers/ 5 hours= 70 km/hr.
So that would be the answer.
The local police department must write, on average, 5 tickets a day to keep department revenues at budgeted levels. suppose the number of tickets written per day follows a poisson distribution with a mean of 6.5 tickets per day. interpret the value of the mean.question 3 options:
Find the area of a circle with the diameter of 3 centimeters use. 3.14 for pi
James built a small electric car and recorded the distance it traveled. The table below shows the distance traveled (n) during the first 4 seconds after starting (f). Elapsed Time (seconds) Distance Traveled (feet) 1 6.2 2 12.4 3 18.6 4 24.8 Which of the following equations represents the relationship between the distance traveled and the elapsed time? f = 6.2 + n n = 6.2 + f f = 6.2n n = 6.2f
jerome burned 75 calories in 15 minutes on a stationary bicycle. how many calories will he burn in 25 minutes?
Bank of america customers select their own three-digit personal identification number (pin) for use at atms.(b) if zero can be the first digit and the numbers can be repeated, what is the probability mr. jones and mrs. smith select the same pin?