12x = 10x + 3
Subtract 10x from both sides
2x = 3
Divide by two on each side
x = 3/2 or 1 1/2 hours
Distance of the trip:
12 * 2 * 3/2 = 36 miles
How long does the trip take:
3/2 + 3/2 + 3/10 = 3 3/10 hours
3 hours
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A rectangular swimming pool has a volume capacity of 2160 cubic feet. Water is being added to the pool at a rate of about 20 cubic feet per minute. Determine about how long it will take to fill the pool completely if there were already about 1200 gallons of water in the pool.
Answer:
Step-by-step explanation:
y=mx+b
2160=20x+60.417)
2160= 20x+160.417
2160-160.417=20x+160.417-160.417
1999.583=20x
1999.583/20=20x/20
x= 99.98 min
Total time taken to fill the pool is 100 minutes
Given:
Amount of water already in pool = 1200 gallon
Total capacity of pool = 2160 cubic feet
Rate of water supply = 20 cubic feet per minute
Find:
Total time taken to fill the pool
Computation:
1 cubic feet = 7.5 gallon water
Amount of water already in pool = 1200 / 7.5
Amount of water already in pool = 160 cubic feet
Remain volume = 2160 - 160
Remain volume = 2000 cubic feet
Total time taken to fill the pool = 2000 / 20
Total time taken to fill the pool = 100 minutes
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what is the digit in the tenths place 15.16 ?
What is the margin of error for a sample statistic for a population with a standard deviation of 11.3?
The margin of error for a sample statistic requires the population standard deviation, the desired confidence level, and the sample size. It is found by multiplying the z-score for the confidence level with the standard error, which is the population standard deviation divided by the square root of the sample size. For a 95% confidence interval, the error bound is factored into the sample mean to estimate the population mean.
The margin of error for a sample statistic depends on the level of confidence desired and the sample size. Using the population standard deviation, we can calculate the margin of error by finding the z-score associated with the desired confidence level and multiplying it by the standard error. The standard error is calculated as the population standard deviation (11.3) divided by the square root of the sample size (n).
Based on the example given referencing an error bound for the mean (3.2), a 95% confidence interval could be constructed by adding and subtracting the error bound from the sample mean (15). Therefore, the 95% confidence interval estimate for the population mean would be (11.8, 18.2).
When a sample standard deviation is provided instead of a population standard deviation, and if the sample size is small, the Student's t-distribution should be used instead of the normal distribution.
For a 95% confidence interval, we generally use 1.96 as the z-score for a normal distribution, but this value could change depending on specific confidence levels or other distributions like the t-distribution.
∠DFG and ∠JKL are complementary angles. m∠DFG = x + 5, and m∠JKL = x − 1. Find the measure of each angle.
∠DFG and ∠JKL are complementary angles
Measure of each angle
[tex]m<DFG=48\\m<JKL= 42[/tex]
Given :
∠DFG and ∠JKL are complementary angles. m∠DFG = x + 5,
and m∠JKL = x − 1
When two angles are complementary then the sum of angles is 90 degrees
∠DFG and ∠JKL are complementary angles.
So, [tex]m<DFG+m<JKL =90[/tex]
Now replace the expressions and solve for x
[tex]x+5+x-1=90\\2x+4=90\\2x=90-4\\2x=86\\x=43[/tex]
Now replace x with 43 and find out each angle
[tex]m<DFG= x+5\\m<DFG= 43+5=48\\\\m<DFG=48\\m<JKL=x-1=43-1=42[/tex]
[tex]m<DFG=48\\m<JKL= 42[/tex]
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How to solve this? I know how to do the Pythagorean theorem but this only gives 1 side
Estimate instantaneous rate of change of the point indicated p(x) = 3x^2-5, x = 2
At Crescent High School, 120 students plan on going to an in-state college and 70 students plan on going to an out-of-state college. What is the ratio of students planning on going to an in-state college to students planning on going to an out-of-state college?
For the normal distribution, the mean plus and minus 1.96 standard deviations will include about what percent of the observatio
A sector of area 2pi/3 square inches is formed by a central angle of 45 degrees. What is the radius of the circle?
Using the formula for the area of a sector, we substitute provided values to find the radius of the circle. Solving the equation, we find the radius to be √6 inches.
Explanation:
The subject of the question is related to geometry and involves understanding the relationship between the area of a sector and the radius of the circle it is part of. The sector is formed by a central angle of 45 degrees and its area is given as 2π/3 square inches.
In order to find the radius of the circle, we can use the formula for the area of a sector, which is (θ/2π) * πr2, where θ is the central angle, π is a mathematical constant, and r is the radius of the circle.
Considering 360 degrees as 2π radians, the angle is 45 * (2π/360) = π/4 radians. Hence substituting the values in the area equation we get; 2π/3 = (π/4)/2π * πr2. If we solve this equation for 'r', we get r = √6 inches as the radius of the circle.
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Solve for x.
−5x−4(x−6)=−3
-5x -(4x-6) = -3
-5x -4x + 24 = -3
-9x = -27
x= 3
lisha is making headbands using ribbon. she would like to make 12 head bands. Each one requires 15.5 inches of ribbon. She estimates that she will need to buy 160 inches of ribbon is her estimate reasonable? Explain your reasoning and lol I'm not in college i just did that
In a survey, respondents were asked which type of activity they enjoyed most while on vacation. The bar graph shows the responses of males and females.
How many more males than females said that swimming was their favorite activity?
I think it's 2.
Answer:
3 more males than females said that swimming was their favorite.
Step-by-step explanation:
We have been given a bar graph in which blue box represents Male and orange box represents Female.
We need to tell how many more males than females said that swimming was their favorite
Number of female in swimming are: 9
And number of male in swimming are: 12
So, we need to find how many more male that means: 12-9=3
That means 3 more males.
To make yummy fruit punch,use 2 cups of grape juice for every 3 cups of apple juice. If you already have 12 cups of apple juice,how many cups of grape juice how many cups will you need to make fruit punch?
To make fruit punch with a given ratio of 2 cups of grape juice for every 3 cups of apple juice, you will need 8 cups of grape juice to mix with 12 cups of apple juice.
Explanation:To answer how many cups of grape juice will be needed when you have 12 cups of apple juice to make a fruit punch, you first look at the ratio given for the punch, which is 2 cups of grape juice for every 3 cups of apple juice. The question provides us with a ratio: 2 cups of grape juice to 3 cups of apple juice. To maintain this ratio with 12 cups of apple juice, we will have to calculate the equivalent amount of grape juice.
Set up a proportion like this:
2 cups grape juice / 3 cups apple juice = x cups grape juice / 12 cups apple juiceCross-multiply to find the value of x:
3 * x = 2 * 123 * x = 24x = 24 / 3x = 8Therefore, you will need 8 cups of grape juice to make the fruit punch with your 12 cups of apple juice.
Find the mean, median, and mode for the data set. Round answers to the nearest tenth if necessary
The mean of the dataset is 9.3, the median is 10, and the mode is 13.
To find the mean, median, and mode of the data set 15, 13, 9, 9, 7, 1, 11, 10, 13, 1, 13, follow these steps:
1. Mean
Add all the numbers together:⇒ 15 + 13 + 9 + 9 + 7 + 1 + 11 + 10 + 13 + 1 + 13 = 102
Divide by the number of values in the data set:⇒ 102 ÷ 11 = 9.3 (rounded to the nearest tenth)
The mean is 9.3.
Median
First, arrange the numbers in ascending order: 1, 1, 7, 9, 9, 10, 11, 13, 13, 13, 15
Find the middle number:The 6th number (since there are 11 numbers) is 10.
The median is 10.
Mode
Identify the number(s) that appear most frequently:In this data set, 13 appears three times.
The mode is 13.
Complete question:
Find the mean, median, and mode of the data set. Round to the nearest tenth. 15, 13, 9, 9, 7, 1, 11, 10, 13, 1, 13
Multiple choice strategy: some students have suggested that if you have to guess on a multiple-choice question, you should always choose
c. carl, the student, wants to investigate this theory. he is able to get a sample of past tests and quizzes from various teachers. in this sample there are 110 multiple-choice questions with four options (a, b, c, d). the distribution of correct answers from this sample is given in the frequency table below. correct answer frequency a 22 b 26 c 38 d 24
What is the GCF of 72 and 36?
Last year, there were 12,000 students at a local college. There were 2000 more female students than male students. How many male and female students attended the college?
A point is located in a polar coordinate system by the coordinates r = 2.8 m and θ = 18°. find the x- and y-coordinates of this point, assuming that the two coordinate systems have the same origin.
You would like to join a fitness center. Fit-N-Trim charges $80 per month. Fit-For-Life charges a one tim e membership fee of $75 and $55 per month. The lines shown in the graph represent the cost y to attend each fitness center for x months. Are the lines parallel?
a line that intersects the points (-23,-17) and (-13,-7), find the slope, now fill in the missing inputs to the slope-intercept formula -17=1(?)+b or (?)=(-13)+b
Which diagram suggests a correct construction of a line that is parallel to given line l and passes through given point q?
1. Draw the perpendicular line to the given line that passes through the point Q. With this aim you should draw a circle with center at point Q and radius that is greater than distance form point Q to the given line. Then match these two points of intersection of this circle with given line as A and B and draw two circles with centers at points A and B and radii that are greater than half of distance between points A and B. These two circles will intersect, combine two points of intersection of these points, this line will be perpendicular to given line.
2. Draw a circle with center at Q and match two points of intersection with perpendicular as E and F.
3. Draw two circles with centers at points E and F and radii that are greater than radius of previous circle. Combine two points of intersection of these circles, this line will be parallel tj the given line.
Taking into account the solution, you can conclude that correct choice is B.
To correctly construct a line parallel to line l through point q, mark point q, use a straightedge to extend from q, and then use a compass to copy the angle and distance from line l, ensuring the newly drawn line is parallel to l.
To construct a line parallel to a given line l and passing through a given point q, one must follow specific geometric principles. This type of construction is often illustrated in diagrams where the correct application of tools such as a ruler and compass is shown.
First, a point q is marked. A straightedge or ruler is used to draw a line transcending the point q. Then, using a compass, the angle between the original line l and any point on it is copied. The compass's width is set to the distance between two points on line l, and the same distance is marked from point q on the drawn line. A line is then constructed using the copied angle and marking, ensuring the new line is parallel to line l.
This process is comparable to the methods used in various scientific and economic models, such as those discussed in the supplied information, where parallel lines represent equivalent conditions or when shifts in lines are required to indicate changes in intercepts.
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Using the following information, calculate the adjusted cash balance at the end of April.
Bank statement ending cash balance $2,000
General ledger cash balance ending 3,250
Bank monthly service charge 45
Deposits in transit 2,500
Outstanding checks 1,500
NSF check returned with bank statement 205
A.4,000
B.5,500
C.4,250
D.3,000
Answer:
The correct option is D. 3,000
Step-by-step explanation:
On the bank statement, compare the issued checks and deposits shown on the statement to identify uncleared checks and deposits in transitStep 1 : Using the cash balance shown on the bank statement, add back any deposits in transit. : 2000 + 2500 = $4500
Step 2 : Deduct any outstanding checks : 4500 - 1500 = $3000
This will provide the adjusted bank cash balance.
Next, use the company’s ending cash balance, add any interest earned and notes receivable amount.Step 3 : Deduct any bank service fees, penalties, and NSF checks. This will arrive at the adjusted company cash balance : 3250 - (205 + 45) = $3000
After reconciliation, the adjusted bank balance should match with the company’s ending adjusted cash balance.
So, the adjusted cash balance at the end of April is $3000
How would you define the traformation "dilation"? what happens to a shape when it is dilated? What changes? what stays the same?
Choose the correct simplification of the expression (−2x + 10y)(4x − 6y).
−8x2 − 52xy + 60y2
−8x2 + 52xy − 60y2
8x2 + 52xy − 60y2
−8x2 + 28xy − 60y2
Part a give the number of total electron groups, the number of bonding groups, and the number of lone pairs for the geometry depicted in (a). express your answers as integers separated by commas.
It can be deduced that there are 4 electron groups, 4 bonding groups, 0 lone pairs.
What is an eletron?An electron means a very small particle that has a negative charge of electricity and it travels around the nucleus of an atom.
In this case, there are 4 electron groups, 4 bonding groups, 0 lone pairs; there are 5 electron groups, 3 bonding groups, 2 lone pairs; there are 6 electron groups, 5 bonding groups, 1 lone pair.
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how do you solve cos((π/6)x)=0
A 20-foot cable hangs from the top of a building that is 50 feet high. if the cable weighs 2 pounds per foot, how much work is done in lifting up the entire cable to the top of the building?
To find the work done in lifting the entire cable to the top of the building, multiply the weight of the cable by the height of the building.
Explanation:To calculate the work done in lifting the entire cable to the top of the building, we need to find the weight of the cable. The weight of the cable can be found by multiplying the length of the cable (20 feet) by its weight per foot (2 pounds per foot). Therefore, the weight of the cable is 20 feet × 2 pounds per foot = 40 pounds.
The work done in lifting the cable to the top of the building is equal to the product of the weight of the cable and the height of the building. So, the work done is 40 pounds × 50 feet = 2000 foot-pounds.
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How would I find a given triangle where: A=0.1, B=1 and c=9? Thanks in advance.
C=
a=
b=
A college freshmen must take a science course, a humanities course and a mathematics course. If she may select any of 6 science courses, any of 4 humanities and any of 4 mathematics courses, how many ways can she arrange her program? Make a tree diagram and list the possibilities.
F(x, y, z) = x2yz − xyz3, p(2, −1, 1), u = 0, 4 5 , − 3 5 (a) find the gradient of f.
Final answer:
The gradient of the function [tex]F(x, y, z) = x^2yz - xyz^3[/tex] can be found by taking the partial derivatives with respect to each variable x, y, and z.
Explanation:
The gradient of a function is a vector that points in the direction of the steepest increase of the function at a particular point. To find the gradient of the function [tex]F(x, y, z) = x^2yz - xyz^3[/tex], we need to find the partial derivatives with respect to each variable.
The partial derivative with respect to x is: [tex]Fx = 2xyz - yz^3[/tex]
The partial derivative with respect to y is: [tex]Fy = x^2z - xz^3[/tex]
The partial derivative with respect to z is: [tex]Fz = x^2y - 3xyz^2[/tex]