The number of hours that it takes for Paul to do the job alone is of:
6 hours.
How to obtain the time it takes for Paul do to the job alone?The time that it takes for Paul to do the job alone is given by the together rate, which is obtained as the sum of the separate rates.
The rates in the context of this problem are given as follows:
Construction worker: 1/12.Paul: 1/x.Together rate: 1/(x - 2) -> 2 hours less than Paul's alone.Hence the value of x is obtained applying the together rate, and it gives the number of hours that it takes for Paul to do the job alone.
Hence:
1/(x - 2) = 1/x + 1/12
1/(x - 2) = (12 + x)/(12x)
Applying cross multiplication, we have that:
(12 + x)(x - 2) = 12x
x² + 10x - 24 = 12x
x² - 2x - 24 = 0
(x + 4)(x - 6).
Applying the Factor Theorem, the solutions are given as follows:
x + 4 = 0 -> x = -4 -> extraneous solution, as the number of hours cannot be negative.x - 6 = 0 -> x = 6 -> actual solution.More can be learned about the together rate at https://brainly.com/question/27859524
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The Grade 8 students had an
end-of-the-year dance.
The disc jockey charged $85 for setting
up the equipment, plus $2 for each
student who attended the dance.
The disc jockey was paid $197.
How many students attended the dance?
a) Write an equation you can use to
solve the problem.
b) Solve the equation.
c) Check your answer and explain
how you know it is correct.
Answer:
1. You can use the equation 2x + 85 = 197
2. 2x+ 85 =197
-85 -85
-------------------------
2x = 112
/2 /2
------------------------
x = 60
x is the number of students that went to the dance
plug in 60 into x in the equation I gave to check
PQR is an isosceles triangle in which PQ= PR Mand N are points on PQ and PR such that angle MRQ= angle NQR. Prove that triangles QNR and RMQ are congruent.
We have proved that triangles QNR and RMQ are congruent.
What is an isosceles triangle?
An isosceles triangle is a triangle with at least two equal-length sides in geometry. It is sometimes specified as having exactly two equal-length sides, and sometimes as having at least two equal-length sides, with the latter version including the equilateral triangle as a special case.
∠MRQ ≅ ∠NQR . . . . given
QR ≅ RQ . . . . reflexive property
∠PQR ≅ ∠PRQ . . . . property of isosceles triangle PQR
ΔQNR ≅ Δ RMQ . . . . ASA postulate
Hence, we have proved that triangles QNR and RMQ are congruent.
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If log 10 to base 8 = X, evaluate log 5 to base 8 in terms of X.
A. 12X
B. X-14
C. X-13
D. X-12
Answer:
Step-by-step explanation:
Y=4/5x-5
Slope:
Y-intercept:
OBFW Publishers
The Graduate Record Examinations (GRES) are widely used to help predict the performance of applicants to graduate schools.
The scores on the GRE Chemistry test are approximately normal with mean 694 and standard deviation 112.
(a) About what percent of test takers earn a score less than 500 on the GRE Chemistry test?
(b) What proportion of test takers earn a score greater than or equal to 900 on this test?
(c) Estimate the score at the 99th percentile on the GRE Chemistry test.
a) About 4.16% of test takers earn a score less than 500 on the GRE Chemistry test.
b) About 96.64% of test takers earn a score greater than or equal to 900 on the GRE Chemistry test.
c) The estimated score at the 99th percentile on the GRE Chemistry test is approximately 954.512.
To answer these questions, we'll use the properties of the normal distribution and the given mean and standard deviation.
(a) To find the percentage of test takers who earn a score less than 500 on the GRE Chemistry test, we need to calculate the cumulative probability up to the score 500.
z-score = (X - mean) / standard deviation
where X is the score we are interested in.
z-score = (500 - 694) / 112
z-score ≈ -1.732
Now, we look up the cumulative probability for a z-score of -1.732 in the standard normal distribution table or use a calculator to find that the cumulative probability is approximately 0.0416 or 4.16%.
So, about 4.16% of test takers earn a score less than 500 on the GRE Chemistry test.
(b) To find the proportion of test takers who earn a score greater than or equal to 900, we need to calculate the cumulative probability from 900 to positive infinity.
z-score = (X - mean) / standard deviation
where X is the score we are interested in.
z-score = (900 - 694) / 112
z-score ≈ 1.839
Now, we look up the cumulative probability for a z-score of 1.839 in the standard normal distribution table or use a calculator to find that the cumulative probability is approximately 0.9664 or 96.64%.
So, about 96.64% of test takers earn a score greater than or equal to 900 on the GRE Chemistry test.
(c) To estimate the score at the 99th percentile on the GRE Chemistry test, we need to find the value that separates the lowest 99% of the scores from the highest 1%.
We use the z-score formula to find the z-score corresponding to the 99th percentile:
z-score = invNorm(0.99)
z-score ≈ 2.326
Now, we use the z-score to find the score corresponding to the 99th percentile:
X = mean + (z-score * standard deviation)
X = 694 + (2.326 * 112)
X ≈ 694 + 260.512
X ≈ 954.512
So, the estimated score at the 99th percentile on the GRE Chemistry test is approximately 954.512.
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Write 5/3 as a mixed number.
Answer:
Step-by-step explanation:
the answer would be 1 and 2/3
3 goes into 5 one time and you have 2 left
keisha is catering a luncheon. She has $30 to spend on a mixture of Cheddar cheese and Swiss cheese. How many pounds of cheese can Keisha get if she buys only Cheddar cheese? Only Swiss cheese? A mixture of both cheeses? What linear equation in STANDARD FORM can she use to model the situration?
Cheddar Cheese: $3/lb
Swiss Cheese: $5/lb
Answer:
Only cheddar 10 pounds
Only swiss 6 pounds
Use the equation to find out different combinations.
3x + 5y = 30
For example, 1 pound of cheddar and 5.4 pounds of swiss.
Step-by-step explanation:
Let x = cheddar
Let y = swiss
3x + 5y = 30
If we only wanted cheddar let y be 0
3x =30 Divide both sides by 3
x = 10
You can buy 10 pounds of cheddar.
If we only wanted swiss let x be 0
5y = 30 Divide both sides by 5
y = 6
You can buy 6 pounds of swiss.
1 pound of cheddar:
3(1) + 5y = 30 Subtract 3 from both sides
5y = 27 Divide both sides by 5
y = 5.4
A 16-ounce bottle of water from Store A costs $1.28. The cost in dollars, y, of a bottle of water from Store B is represented by the equation y=0.07x, where x is the number of ounces. What is the cost per ounce of water at each store? Which store's bottle of water costs less per ounce?
The cost of per ounce of water at store A is $0.08 and at store B is $0.07 , the water in the store B will cost less per ounce .
In the question ,
it is given that
in store A the cost of 16 ounce of water is $1.28 ,
so the cost of 1 ounce of water in store A is = 1.28/16
= $0.08
in store B the cost of water is represented by the equation
y = 0.07x
where "x" is the number of ounces of water ,
which means
the cost of 1 ounce of water in store B is = $0.07
hence , the water in store B will cost less .
Therefore , The cost of per ounce of water at store A is $0.08 and at store B is $0.07 , the water in the store B will cost less per ounce .
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suppose you have 6 pairs of sock in your sock drawer and every pair has a unique color. it is still dark out in the morning when you get dressed, so you just pull socks out of the drawer at random, one at a time, until you have removed two matching socks. what is the probability that you pull out exactly 5 socks from your sock drawer in the morning before you get a matching pair of socks?
The probability there is at least one pair is therefore 1−p.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.acc to our question-
It is little known, but socks have individual identities. There are (166) equally likely ways to choose 6 socks from the 16.Now we find the number of ways to choose 6 socks, so that there is no pair among them. There are (86) ways to choose the "types" of sock we will have. For each choice of 6 types, there are 26 ways to choose the actual socks. For at each chosen "type" of sock, we have 2 choices as to which of the two socks of that type to take.hence,The probability there is at least one pair is therefore 1−p.
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A right triangle has coordinates (-3, 4), (3,6), and (-1,-2). What is the area of the right triangle?
help
Answer:
2728
Step-by-step explanation:
Answer:
20 sq units
Step-by-step explanation:
A quick sketch graph will show the right angle is at (-3 ,4)
The lengths of the shorter sides are both sqrt(2^2 + 6^2) = sqrt(40)
Area = 1/2 x (sqrt(40))^2 = 20
If you didn’t have a right angle you could find the lengths of all sides a, b and c
Calculate the semi perimeter s = (a+b+c) / 2
And the area = sqrt(s(s-a)(s-b)(s-c))
Try and use this method to check the first one
An equation is shown:
−np − 4 = 2(c − 3)
Which of the following solves for n?
n = the quantity 2 times c plus 2 all over negative p
n = the quantity 2 times c plus 10 all over negative p
n = the quantity 2 times c minus 2 all over p
n = the quantity 2 times c minus 10 all over p
The solution of given equation for n would be n = (2c - 2)/(-p)
In this question, we have been given an equation.
We solve given equation for n.
−np − 4 = 2(c − 3)
−np − 4 + 4 = 2(c − 3) + 4
−np= 2c - 6 + 4
-np = 2c - 2
np = -2c + 2
np * 1/p = (-2c + 2) * (1/p)
n = (-2c + 2)/p
n = (2c - 2)/(-p)
Therefore, the solution of given equation for n would be n = (2c - 2)/(-p)
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Answer:
The answer would be n = (2c - 2)/(-p)
Step-by-step explanation:
Hope this helps! :D
Find the area of the sas triangle with side lengths 29 and 36 and included angle 62 degrees.
To find the area of the sas triangle with side lengths 29 and 36 and included angle 62 degrees.
Area of the sas triangle with side lengths 29 and 36 and included angle 62 degrees is 459.36.
A triangle's feature known as SAS, or "Side, Angle, Side," has two sides and an angle that are both known.
The space occupied between the sides of the SAS triangle in a plane can thus be calculated with the use of the SAS triangle area formula.
The formula to find area of SAS triangle is:
Area = ½ ab Sin C = ½ × 29 × 36 × sin 62
Thus, Area = 522 × sin 62 = 522 × 0.88 = 459.36
Hence the answer is, Area of SAS triangle with side lengths 29 and 36 and included angle 62 degrees is 459.36.
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The legs of an isosceles triangle are 0.3 foot less than twice the base. The perimeter of the triangle is 4.9 feet.
What is the length of one of the triangle’s legs?
A. 1.1 feet
B. 1.4 feet
C. 1.9 feet
D. 2.2 feet
Answer:
it's D of the triangles legs this is the answer
you have 3 bags of candy each with 4 pieces of candy in them. How many pieces of candy do you have?
Answer:
12
Step-by-step explanation:
3x4
A pair of jeans at a local retail store has a cost of $32.00. If the sales tax is 5.3%, what is the total amount paid for the jeans?
The total amount that a customer will pay for the jeans is $33.696.
How to calculate the value?From the information given, pair of jeans at a local retail store has a cost of $32.00. If the sales tax is 5.3%,
The value of the sales tax will be:
= Sales percentage × Amount
= 5.3% × $32
= $1.696
The total amount paid will be:
= Cost + Tax
= $32 + $1.696
= $33.696
The amount is $33.696.
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Find the value of the specified trig ratio. Be sure to reduce when possible.
The value of cosC is 8/17.
What is the trigonometric ratio?
Trigonometric ratios are the ratios of a right triangle's sides. The sine (sin), cosine (cos), and tangent (tan) are three often used trigonometric ratios. There are other trigonometric ratios which are reciprocals of these ratios.
Trigonometric ratios can be computed either using the provided acute angle or by calculating the ratios of the right-angled triangle's sides.
In the figure,
Adjacent=CB=16
hypotenuse=AC=34
The formula for the cos function:
cos[tex]\theta[/tex]=adjacent/hypotenuse
cosC=16/34
divide 16 and 34 by 2 to simplify further
cosC=8/17
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my last question for marth
The equation of linear function is y=x-1.
What is equation of line?A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.
The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.
The given values are
x=1, y=0
x=2, y=1
x=3, y=2
x=4, y=3
The table represents that for the value of x the value of y is x-1,
Since for any two points from the table, let (1,0) and (2,1)
The slope = 2-1/1-0 = 1
And the interception of y is 0 when x=1
Therefore, the equation of the function can be written as,
y=x-1
Y=x-1 is the required equation.
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tiffany walks x miles in 90 minutes. How many miles can she walk in 120 minutes?
A. 4/3 x
B. 30x
C. 3/4
D. 0.75x
Answer: A. 4/3 x
Step-by-step explanation:
x miles in 90 minutes to ? miles in 120 minutes
90 miles to 120 miles is 1.3333 which is equal to 4/3.
Multiply it to x and you have A. 4/3x
f(x) = 0.75(10-x)+1
Someone help please
The solution for f(3) in the function when the function f(x) = 0.75(10 - x) + 1 is 6.25
How to determine the solution for f(x) in the function?From the question, we have the following equation that can be used in our computation:
f(x) = 0.75(10-x)+1
To make the equation legible, we need to rewrite it
So, we have the following representation
f(x) = 0.75(10 - x) + 1
Also from the question, we have
f(3)
This means that the value of x is 3, and we calculate f(x) when x = 3
Substitute the known values in the above equation, so, we have the following representation
f(3) = 0.75(10 - x) + 1
So, we have the following equation
f(3) = 0.75(10 - 3) + 1
There are constants to add or subtract to both sides of the equation
Also, there are factors to multiply or divide from both sides of the equation
So, we have the following representation
f(3) = 0.75 * 7 + 1
Solving further, we have
f(3) = 5.25 + 1
Evaluate the sum
f(3) = 6.25
Hence, the solution is 6.25
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Possible question
Given f(x) = 0.75(10-x)+1, find f(3).
?
Answer the question below. Type your response in the
space provided.
Does your state have a sales tax?
Find the area of a rectangle whose side lengths are 8x² feet and 8x³ feet.
A.The area of the rectangle is 16x² feet squared.
B. The area of the rectangle is 64x5 feet squared.
C.The area of the rectangle is 16x² + 16x³ feet squared.
D.The area of the rectangle is 16x5 feet squared.
Answer:
ccccccccc
Step-by-step explanation:
Write an equation in slope-intercept form of the line with the given
characteristics.
slope = 2/5
; passes through (–3, 1)
Answer:
The equation of the line in slope-intercept form is [tex]y=0.4x+2.2[/tex]
Step-by-step explanation:
The equation of the line in slope-intercept form can be calculated as follows ?
The first step is to find the slope-intercept form of the given line by the point-slope form formula as follows
[tex]y-y_{1}=m(x-x_{1})[/tex]
Where [tex]m[/tex] is the slope of the line
Write the given value of the slope
[tex]m=\frac{2}{5}[/tex]
Convert the value of the slope into decimal
[tex]m=0.4[/tex]
The second step is to substitute [tex]0.4[/tex] for [tex]m[/tex], [tex]1[/tex] for [tex]y_{1}[/tex], [tex]-3[/tex] for [tex]x_{1}[/tex] in the point-slope form formula
[tex]y-1=0.4(x-(-3))[/tex]
Take out the inner bracket on the right side of the equation
[tex]y-1=0.4(x+3)[/tex]
Expand the right side of the equation
[tex]y-1=0.4x+1.2[/tex]
Add [tex]1[/tex] to both sides of the equation
[tex]y-1+1=0.4x+1.2+1[/tex]
Simplify the equation
[tex]y=0.4x+2.2[/tex]
Hence the equation of the line in slope-intercept form is
[tex]y=0.4x+2.2[/tex]
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How many students catch the train?
Thank you for helping.
Answer:
35
Step-by-step explanation:
18+17=35
Charlotte is making 6 pounds of trail mix using raisins and 3 different types of nuts.
The table shows the amounts of different types of nuts that she has.
Type of Nut Amount (in pounds)
almonds
7
8
cashews
1
1
2
peanuts
2
3
8
pecans
1
1
4
walnuts
1
3
4
Charlotte uses all of the almonds, cashews, and peanuts that she has.
Which of the following explains how she can find the exact amount of raisins she needs?
A.
Round
7
8
pound to 1 pound,
1
1
2
pounds to 2 pounds, and
2
3
8
pounds to 2 pounds.
Then add the rounded amounds and subtract that total from 6 pounds.
B.
Add
7
8
pound,
1
1
2
pounds,
2
3
8
pounds,
1
1
4
pounds, and
1
3
4
pounds.
Then subtract 6 pounds from that total.
Answer:
It Should be B because You need to add all of the pounds and subtract it by six
Step-by-step explanation:
what is the slope of a line that passes through the points (-1, -3) and (-19,-18)
The slope of the line that passes through the points (-1, -3) and (-19,-18) is 16/17.
slope of a line :
the measurement of a line's direction in a coordinate plane.It is denoted by m.m = (y₂ - y₁)/(x₂ - x₁)m = tanθA = (x₁, x₂) = (-1, -3)
B = (y₁, y₂) = (-19,-18)
The slope of a line is given as :
slope = (y₂ - y₁)/(x₂ - x₁)
slope = (-19 - (-3))/(-18 - (-1))
slope = (-19 + 3)/(-18 + 1)
slope = ( -16 )/ ( -17)
slope = 16/17.
The slope of the line that passes through the points (-1, -3) and (-19,-18) is 16/17.
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URGENT: If a pack of five compasses sells for $3.95,
How much does one compass cost?
Answer:
0.79 dollars
Step-by-step explanation:
Divide 3.95 by five to find the cost of one compass.
Solve inequality 2(5-x)-6<15-4x-9
Answer:
x<1
Step-by-step explanation:
10-2x-6<15-4x-9 (distributive property)
4-2x<6-4x (simplified both sides)
-2x<2-4x (1st step to get x isolated)
2x<2 (2nd step to get x isolated)
x<1 (divide 2 from each side)
and that's how! :)
2- Which equations have no solution? Select all
that apply.
x + 3 = 2x + 3
8 = 2(x+4) − 2x.
5x-2x = -7x+1
2x-3 = 5x - 3-3x
4xx+6= 2(x+1)+x
Answer: E has no solution
Step-by-step explanation: It is a contradiction
what is the t-multiplier for a 95% confidence interval for a population mean, using a well-behaved sample of size 14? r lab
The appropriate t-multiplier for a 95% confidence interval for the mean μ is t(0.025,14) = 2.15.
Given:
The t-multiplier for a 95% confidence interval for a population mean, using a well-behaved sample of size 14.
It is the 97.5%-quantile of the t-distribution with 14 degrees of freedom.
In the figure the dashed line shows the value such that the yellow shaded area has size 0.975: the 97.5%-quantile is the value such that 97.5% of the probability mass is to the left of it and the rest to the right.
so t - multiplier = 2.15.
Therefore the appropriate t-multiplier for a 95% confidence interval for the mean μ is t(0.025,14) = 2.15.
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Which best describes the range of the function f x 2 3 x?.
The range of the function f(x) = 2(3)x is best described by y > 0. Particularly the function when the constant is e, a function whose value is a constant raised to the power of the argument.
What is range of function?The difference between the lowest and highest values in a list or set is known as the range. Put all the numbers in order before determining the range. The lowest number should then be subtracted from the highest. The range of the list is provided in the response. The difference between the highest and lowest values for a particular data collection is the range in statistics. For instance, the range will be 10 - 2 = 8 if the provided data set is 2, 5, 8, 10, and 3. As a result, the range may alternatively be thought of as the distance between the highest and lowest observation.
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