Hours taken by Bob and Bill if they work together is 3 1/13.
Here it is given that Bob can do a job in 5 hours and Bill can do the job in 8 hours.
We have to find the time taken by both to do the work if done together.
Time ratio of Bob and Bill = 5: 8
Efficiency of Bob and Bill = 8: 5
Total amount of work done = 5× 8 = 8× 5 = 40
The total efficiency of Bob and Bill = 13
Hours took by both bob and bill to do the work if done together = 40/13
= 3 [tex]\frac{1}{13}[/tex]
Therefore the work done together is 3 [tex]\frac{1}{13}[/tex] hours.
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according to a wired magazine article, of e-mails that are received are tracked using software that can tell the e-mail sender when, where, and on what type of device the e-mail was opened (wired magazine website). suppose we randomly select received e-mails. a. what is the expected number of these e-mails that are tracked?
There should be 12 emails total.
7.200 and 2.683 are the variance and standard deviation, respectively.
What is varience?The statistical assessment of the variation in numbers within a data collection is known as variance. In more detail, variance assesses how far apart each number in the collection is from the mean (average) and, consequently, from each other. This symbol is frequently used to represent variation: 2. Both analysts and traders use it to assess market volatility and security.The standard deviation (SD or ), which aids in determining the consistency of an investment's returns over time, is the square root of variance.Calculation of expected number of emails, variance and standard deviation:
Given thatP = 0.40 and n = 30a)The expected value of received e-mails is= n × p= 30 × 0.4= 12 b)The variance of emails received is= n × p × (1 - p)= 30 × 0.4 × 0.6= 7.200NowThe standard deviation of emails received is= sqrt(variance)= 2.683Learn more about variance here:
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in order to estimate the proportion of all credit card holders who pay their credit card bills in full each month a credit counseling bureau took a random sample of 450 credit card holders and found that 127 pay all their credit card bills in full each month. a 99% confidence interval for the proportion of all credit card holders who pay all their credit card bills in full each month is:
A 99% confidence interval for the proportion of all credit card holders who pay all their credit card bills in full each month is 0.282 + 0.055.
Define confidence interval.Confidence intervals, which describe how closely study results match reality or how dependable they are based on statistical theory, are regularly mentioned in scientific publications. The sample is used to calculate the confidence interval, which represents the range of likely population parameters. In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time.
Given,
Number of credit card holders
n = 450
x = 127
p = 127/450
Proportion:
p = 0.2822
99% confidence interval:
C I = 0.2822 ± 2.576 × 0.2122
CI = 0.2822 ± 0.05465
CI = 0.282 + 0.055
A 99% confidence interval for the proportion of all credit card holders who pay all their credit card bills in full each month is 0.282 + 0.055.
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Write an equation of the line in slope-intercept form.
Ay
4
y =
(0, 2)
2
(3, 3)
4
AX
Equation of line in slope-intercept form is [tex]y = (\frac{1}{3})x + 2[/tex].
Given in graph,
A(0,2) and B(3,3)
Slope-intercept form => y = mx + c
Slope, m = [tex]\frac{y2-y1}{x2-x1}[/tex]
= [tex]\frac{3-2}{3-0}[/tex]
= [tex]\frac{1}{3}[/tex]
Therefore, y = (1/3)x + c
Put A(0,2) in above equation
2 = (1/3)*0 + c
2 = c
Hence, y = (1/3)x + 2.
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A hippopotamus can run 6 kilometers in 15 minutes. At this rate, how far can the hippopotamus run in 1 minute?
Answer:
400meters
Step-by-step explanation:
Find the speed of the hippopotamus by dividing distance with time
6000 meters ÷15minutes =400meters/minutes
how do you simplify the distributive property ?
Answer:
for example 2(3+1)
to solve with the distributive property you multiply the number outside the parentheses(2) with each inside number(3 and 1) individually.
2(3)+2(1)
now solve
6+2=8
now to check it by solving the regular way
2(3+1), 3+1=4 so
2(4)
8
we can see that the answers are the same.
to use the distributive property with x in it
for example, -3(x-6)
multiply the outside number(-3) with each inside number(x and -6)
-3(x)+(-3)(-6)
simplify
-3x-(-18)
-3x+18
hope this helps!
Bloomington University charges $53,730 for tuition. If they raise their tuition by 8% each
year, how much will tuition be in 2 years?
If necessary, round your answer to the nearest cent.
$
E
I need to know before I can perform a rotation.
the size of the coordinate plane
the degree of rotation
which way to flip the point, line, or figure
which way to slide the point, line, or figure
To perform Rotation in coordinate plane the following information may help you.
What is Geometric Rotation ?
In geometry, rotation is a type of rigid motion or transformation that involves the movement of a shape about a point while preserving the shape, size, and distance between the points on the shape.The center of rotation is the location around which the shape is rotated.
To perform Rotation in coordinate plane
The size of the coordinate plane - the points or graph is mention in question so no need to worry about size of coordinate plane.The degree of rotation : This describes the extent to which a shape is rotated, and can vary from 0° to 360°. This is a required condition to know when to stop rotating the figure.Last two questions sum up and I'm explaining like that,
Reflection in the line y = 0 [x - axis]When a point is reflected in the x-axis then signs of it's ordinate (y-axis) change.
Mₓ (x, y) = (x, - y)
Reflection in the line x = 0 [y - axis]When a point is reflected in the y-axis then signs of it's abscissa (x-axis) change.
My (x, y) = (-x, y)
Reflection in the originWhen a point is reflected in the origin , the signs of it's Abscissa and ordinate change.
M₀ (x, y) = (-x, -y) (in origin the sign become opposite if there is '+' then it changes to '-' and vice versa)
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2. The lengths of a certain species of fish was
found to be normally distributed. The mean
length is 78 cm with a standard deviation
of 14 cm. In a school of 370 of these fish,
how many would be longer than than
92 cm
So, approximately 59 fish in the school would be longer than 92 cm.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides separated by an equal sign (=). The expressions on both sides of the equal sign can contain variables, constants, coefficients, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, logarithms, etc.
Here,
We can solve this problem using the normal distribution formula, which states:
z = (x - mu) / sigma
where z is the standard score, x is the raw score, mu is the mean, and sigma is the standard deviation.
To find the number of fish longer than 92 cm, we need to find the proportion of fish in the population with lengths greater than 92 cm. We can then multiply this proportion by the total number of fish in the school to get the number of fish longer than 92 cm.
First, we calculate the standard score for 92 cm:
z = (92 - 78) / 14
z = 1
Next, we look up the proportion of the standard normal distribution that corresponds to a z-score of 1. We can use a standard normal distribution table or calculator to find this value. The proportion of the distribution that is greater than z = 1 is approximately 0.1587.
Therefore, the proportion of fish in the population with lengths greater than 92 cm is 0.1587. To find the number of fish longer than 92 cm, we multiply this proportion by the total number of fish in the school:
370 * 0.1587 = 58.8
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find the slope through(0,10) and (24, 6)
Answer:
slope = - [tex]\frac{1}{6}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 10 ) and (x₂, y₂ ) = (24, 6 )
m = [tex]\frac{6-10}{24-0}[/tex] = [tex]\frac{-4}{24}[/tex] = - [tex]\frac{1}{6}[/tex]
Write the equation of a line in point slope form that has a slope of 1/3 and passes through the point (6,-2)
The equation of a line in the point-slope form that has a slope of 1/3 and passes through the point (6,-2) is [tex]y+2 =\frac{1}{3} (x-6 )[/tex].
What is point-slope form?A straight line is represented using its slope and a point on the line using point slope form. In other words, the point-slope form is used to determine the equation of a line whose slope is "m" and passes through the point ([tex]x_{1}, y_{1}[/tex]). The equation of a straight line can be expressed in various ways, Point slope shape is one of them. The point slope form's equation is as follows:[tex]y-y_{1} =m(x-x_{1} )[/tex]where (x, y) is a chance point on the line that should be treated as a variable when using the formula.A fixed point on the line is ([tex]x_{1}, y_{1}[/tex]).The slope of the line is m.Calculation
[tex]y-y_{1} =m(x-x_{1} )[/tex]
[tex]y-(-2) =\frac{1}{3} (x-6 )[/tex]
[tex]y+2 =\frac{1}{3} (x-6 )[/tex]
Therefore, the equation of a line in the point-slope form that has a slope of 1/3 and passes through the point(6, -2) is [tex]y+2 =\frac{1}{3} (x-6 )[/tex]
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GHLJ and GSTU are both parallelograms. Why is
∠L ≅ ∠T?
Parallelogram G S T U is inside of larger parallelogram G H L J. Side G S in on side G H, and side G U is on side G J.
The angle L is congruent to angle T ∠L ≅ ∠T and the reason is that opposite angles of a parallelogram are congruent.
How to identify congruent angles?We are given the parallelograms GHLJ and GSTU in such a manner that the parallelogram GSTU is inscribed right inside parallelogram GHLJ with angle G coinciding on the two parallelograms.
Now, we can remember that property of parallelogram states that the opposite angles of a parallelogram are congruent.
Thus, angle G is congruent to angle T and angle L .
Therefore, ∠L ≅ ∠T
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Answer:
By the parallelogram angle theorem, opposite angles of a parallelogram are congruent. Therefore, angle T must be congruent to angle G, and angle G must be congruent to angle L. By the transitive property of congruence, angle T is congruent to angle L.
Step-by-step explanation:
got it right on edge2
Triangles UVW and VUX are congruent identifier common sides are angles.
Answer:
Common side: UV
Step-by-step explanation:
This rectangular design is made from 6 squares. there are 2 small squares surrounded by 4 larger squares. the area of each small square of 1sq.cmwhat is the total area of the design?
The total Area the design is 8 square cm.
Area of rectangular design is product of length and breadth of rectangular design.
In the given question we have,
Rectangular design is made up from 6 squares .
there is 2 small squares surrounded by 4 large squares.
Area of each small square = 1 sq.cm
let the length of rectangular design be l cm
and breadth is b cm.
Area of rectangular design= l×b sq.cm
from the given statement, we can see that side of small square is 1 cm and small squares surrounded by 4 large squares i.e side of large square is sum of side of small squares or 2cm .
Also , length of rectangular design is sum of sides of two large squares and breadth is same as side of one large square.
so, length of rectangular design= 4 cm
breadth of rectangular design= 2cm
Area of rectangular design= 4×2 = 8sq. cm
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Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease y=210(1.092)^x
The change y=210(1.092)^x represent exponential growth
The percentage rate of increase is 9.2 percent increase
How to determine exponential growthExponential functions are functions that consist of three part say c(b)^d
the part that says whether the function is growth or decay is b
b is called the base function and it is used as follows to determine growth or decay function
b < 1 gives a decay functionb > 1 gives a growth functionComparing with the given function 1.092 > 1 hence a growth function
The percentage is solved as follows
1.092 * 100 = 109.2%
109.2% is also referred to as 9.2 percent increase since it is an increment of 9.2%. this is shown below
100% + 9.2% = 109.2%
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What is the
y-intercept of the function f(x)=-2/9x+1/3?
Answer:
1/3
Step-by-step explanation
We can immediately tell the y-intercept is 1/3.
Slope intercept form:
y = mx + b
m = slope
b = y-intercept.
Answer: the y - intercept is 1/3
Step-by-step explanation: trust
Jared has earned 23% of the $52 he needs to buy a new jacket. Find 23% of $52.
Which expression can you use to find 23% of 52?
0.23 × 52
23% of $52 is $
11.96
.
An easy way to check your answer is to use the friendly
50%
and divide 52 by
2
to get
13
.
Am i right???
Answer:
yeah i think so
Answer:
$11.96
Step-by-step explanation:
Now we have to,
→ find the 23% of $52.
Let's solve the problem,
→ 23% of $52
→ (52/100) × 23
→ 0.52 × 23
→ $11.96
The similar expression is,
→ 0.23 × 52
→ $11.96
Hence, answer is $11.96.
two cars are traveling in the same direction along the same route. the red car travels at a constant speed of 40 miles per hour, and the black car is traveling at a constant speed of 50 miles per hour. if the red car is 20 miles ahead of the black car, how many hours will it take the black car to overtake the red car?
Balck car can overtake the red car in 2 hrs
Relationship between Speed, Distance and Time:
The Relationship between Speed, Distance & Time can be understood by the following formulas
Speed = Distance/Time
Time = Distance / Speed
Distance = Speed X Time
Constant speed:
Constant speed is also called the uniform rate which involves something traveling at a fixed and steady pace or something moving at some average speed.
Here we have
Two cars are traveling in the same direction along the same route.
The speed of the Red car = 40 miles per hr
The speed of the Black car = 50 miles per hr
From above data
The difference between speeds of cars = 50 - 40 = 10 miles per hr
Which means the Black car is chasing the Red car at 10 miles per hr
Given that distance between two cars = 20 miles
The time taken by the Black car to cover 20 miles
=> Distance/ speed = 20/10 = 2hrs
Balck car can overtake the red car in 2 hrs
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help meeeeeeeeeeeeeee pleaseee
The table of solutions for this quadratic equation (y = -2x²) include the following:
x y_
-2 -8
-1 -2
0 -0
1 -2
2 -8
Also, a graph of the solution of this quadratic equation is shown in the image attached below.
How to determine the solution and plot the graph?In Mathematics, the valid and true solutions to the given quadratic equation (y = -2x²) are referred to as ordered pairs and they can be determined by substituting the x-values contained in the table into the quadratic equation as follows;
When x = -2, the y-value for this quadratic equation is given by:
y = -2x²
y = -2(-2)²
y = -2 × 4
y = -8
When x = -1, the y-value for this quadratic equation is given by:
y = -2x²
y = -2(-1)²
y = -2 × 1
y = -2
When x = 0, the y-value for this quadratic equation is given by:
y = -2x²
y = -2(0)²
y = -2 × 0
y = 0
When x = 1, the y-value for this quadratic equation is given by:
y = -2x²
y = -2(1)²
y = -2 × 1
y = -2
When x = 2, the y-value for this quadratic equation is given by:
y = -2x²
y = -2(2)²
y = -2 × 4
y = -8
In conclusion, you would notice that a graph of this quadratic equation is parabolic (u-shaped) in nature with a slope of -2.
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What is the value of x?
1.9x+0.1x=0.6
Enter your answer as a decimal in the box.
x = ???
Answer:
x = 0.3
Step-by-step explanation:
[tex] \sf1.9x + 0.1x = 0.6[/tex]
Combine like terms.
[tex] \sf2x = 0.6[/tex]
Divide both sides by 2.
[tex] \sf \: x = 0.3[/tex]
What is the product of (4i-5)(4i+5)
The product of (4i-5)(4i+5) is -41.
What are complex numbers?
Every complex number can be expressed in the form a + bi, where a and b are real numbers. A complex number is an element of a number system that extends the real numbers with a specific element denoted i, also known as the imaginary unit, and satisfies the equation i² = - 1.
Here, we have
Given function
= (4i-5) (4i+5)
After applying the product rule, we get
= 16i² + 20i - 20i - 25
= 16i² - 25
after putting i² value, we get
= 16(-1) - 25
= -41
Hence, the product of (4i-5)(4i+5) is -41.
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Heeelllllllllllp Simplify the expression completely.
√144 +18 √12-5√64
Answer:
A
Step-by-step explanation:
using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex] , then
[tex]\sqrt{12}[/tex]
= [tex]\sqrt{4(3)}[/tex]
= [tex]\sqrt{4}[/tex] × [tex]\sqrt{3}[/tex]
= 2[tex]\sqrt{3}[/tex]
Then
[tex]\sqrt{144}[/tex] + 18[tex]\sqrt{12}[/tex] - 5[tex]\sqrt{64}[/tex]
= 12 + 18(2[tex]\sqrt{3}[/tex] ) - 5(8)
= 12 + 36[tex]\sqrt{3}[/tex] - 40
= - 28 + 36[tex]\sqrt{3}[/tex]
marrisa bought 3 packages of balloons and 4 packages of party favors for a total of 14.63. Ray bought 2 packs of balloons and 4 packs of party favors for a total of 16.03. find the price of a pack of balloons and the price of a pack of party favors
The price of a pack of balloons is 4. 39
The price of a pack of party favors is 0. 36
How to determine the valuesWe have that;
Let the cost of balloons be x
Let the cost of party favors by y
From the information given, we have that;
3x + 4y = 14. 63 (1)
2x + 4y = 16. 03 (2)
Now, let's make 'x' the subject from equation (1)
x = 14. 63 - 4y/ 3 (3)
Substitute in equation (2)
3( 14. 63 - 4y/ 3) = 16. 03
expand the bracket
43. 69 - 12y /3 = 16. 03
cross multiply
43. 69 - 12y = 48. 09
collect like terms
- 12y = - 4. 4
make 'y' the subject
y = 0. 36
substitute in equation (3)
x = 14. 63 - 4(0. 36)/ 3
x = 13. 1/ 3
x = 4. 39
Hence, the prices are 4. 39 and 0. 36 respectively.
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Given f(x)=2x+4 , describe how the graph of g compares with the graph of f.
g(x)=2(0.4x)+4
Please help
The function g(x) is a horizontal dilation of scale factor k = 5/2 of function f(x).
How the two graphs compare?We know that f(x) is a linear function:
f(x) = 2x + 4
Here we know that:
g(x) = 2*(0.4x) + 4
Notice that function g(x) can be written as:
g(x) = f(0.4*x)
So we have a horizontal dilation, remember a horizontal dilation of scale factor k can be written as:
g(x) =f(x/k)
Notice that 0.4 = 2/5
Then we have a horizontal dilation of scale factor 5/2.
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The sum of the squares of two consecutive positive numbers is 1,105. Find the numbers.
Answer:
23 and 24
Step-by-step explanation:
let the 2 consecutive numbers be n and n + 1 , then
n² + (n + 1)² = 1105
n² + n² + 2n + 1 = 1105 ( subtract 1105 from both sides )
2n² + 2n - 1104 = 0 ( divide through by 2 )
n² + n - 552 = 0 ← in standard form
(n + 24)(n - 23) = 0 ← in factored form
equate each factor to zero and solve for n
n + 24 = 0 ⇒ n = - 24
n - 23 = 0 ⇒ n = 23
However, n > 0 , then n = 23 and n+ 1 = 23 + 1 = 24
the numbers are 23 and 24
Given the following function, find the vertex, y=5x^2-8x+6
Answer:
The vertex is (0.8, 2.8)------------------------------------
GivenFunction y = 5x² - 8x + 6Find the x-coordinate of the vertexx = - b/(2a)x = - (-8)/(2*5) = 8/10 = 0.8Find the y-coordinate of the vertexy = 5(0.8²) - 8(0.8) + 6 = 2.8Can anyone state the vertex of the graph?
The graph has no vertex
The transformations from the parent function are
Vertical shift down 2Horizontal shift left 4How to determine the vertex?To determine the vertex of a graph, we look for the location of the maximum or the minimum point of the graph
Because the graph is a cubic function, the graph has no maximum or minimum (by definition)
This means that there is absence of a vertex in the graph
The transformation from the parent functionIn (a), we have
We can see that the graph is a cubic function
This function is represented as
y = ∛x
In this graph, we can see that the graph is 4 units to the left i.e. y = ∛(x - 4)
And 2 units below the origin i.e. y = ∛(x - 4) + 2
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Write an equation for the transformation of y=x; vertical by a factor of 1/10
The equation the function after the transformation is g(x) = x/10
How to determine the transformation of the function?The equation of the function is given as
y = x
Express as a function
f(x) = x
The sequence of transformations is given as follows:
Vertically stretched by a factor of 1/10
When the above transformations are combined, we have:
Vertically stretched by a factor of 4: g(x) = 1/10f(x)
So, we have
g(x) = 1/10f(x)
Substitute x for f(x)
So, we have
g(x) = 1/10 * x
Evaluate
g(x) = x/10
Hence, the function g(x) is g(x) = x/10
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Stacy bought 8.3 pounds of fruit for a class party. The class ate 7.44 pounds of the fruit. How much fruit is left?
Answer:
0.86 pounds of fruit is left.
Step-by-step explanation:
If Stacey bought 8.3 pounds and the class ate 7.44 pounds, the amount of fruit that's left is 8.3-7.44=0.86
A,B and C form a triangle where ∠BAC=90∘.AB=7 mm and BC=13.8 mm. Find the length of AC, giving your answer rounded to 1 decimal place.
The length of AC which is the hypothenuse is equal 15.5mm
Pythagoras TheoremThe Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle.
In this question, triangle ABC forms a right-angle triangle at angle B and this makes it possible to use Pythagoras theorem.
AB = leg = 7mmBC = leg = 13.8mmAC = hypothenuse = ?Using the formula;
AC² = AB² + BC²
AC² = 7² + 13.8²
AC = 15.5mm
The length of the hypothenuse is 15..5mm
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Divide. Write 5/8 as a fraction, a whole number, or a mixed number.
Answer: 5/8
Step-by-step explanation:
5/8 is already a fraction