Answer:Given
a can do a piece of work = 40 days
so, A's 1 day work =1/4
so, A's 8 day's work =8/40=1/5
remaining work = 1- 1/5= 4/5
Now, B can do 4/5 piece of work in =16 days
So, B’s 1 day's work = (4/5) /16= 4/ 5x6=1/20
Therefore, (A+B)’s 1 day's work = 1/40+1/20 =
1+2/40=3/40
∴ Both (A+B) can do a piece of work in =
1/days (3/40) = 40/3 days
= 13 1/3 days
scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 13. use empirical rule to determine the following:
a) what percentage of people has an IQ score between 61 and 139?
b) what percentage of people has IQ score less than 87 or greater than 113?
c) what percentage of people has an IQ score greater than 113?
Using the Empirical Rule, the percentages are given as follows:
a) 99.7%.
b) 32%.
c) 16%.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.Item a:
61 and 139 is within 3 standard deviations of the mean, hence the percentage is of 99.7%.
Item b:
87 and 113 is within one standard deviation of the mean, hence 68% of the data is within this interval and 100 - 68 = 32% of the data is outside this interval.
Item c:
Considering that the normal distribution is symmetric, and item b, this percentage is of 32%/2 = 16%.
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there are 32 students in a class and 20 of them own at least one pet
what fraction of class own pets?
give your answer in its simplest form.
Answer:
there 32 students and 20 have pets so you take 20 over 30 divide by 2 to get 10/16 then divide by 2 to get 5/8and that is the answer
State. Probability sampling vs. non probability sampling
Probability sampling simply illustrates a scenario where the subjects of the population have an equal opportunity.
What is probability sampling?Probability simply means the likelihood of the occurence of an event.
In this case, in probability sampling, the subjects of the population have an equal opportunity.
In non-sampling, an equal opportunity isn't given.
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The two lines below are parallel. If the slope of the red line is 3, what is the
slope of the green line?
Use the following image to solve the problem
Answer:
The distance is √17.
Step-by-step explanation:
the step is provided in the image....
I hope it was helpful
Can anyone explain this answer, I'll give brainliest.
Where does the 0.693 and 2.303 come from?
The constants 0.693 is the natural log of 2 and the constant 2.303 is the multiplicative factor of converting log of a number to the natural log of that same number.
What are 0.693 and 2.303 used for?It follows from the task content that the calculation involves the use of the half-life of radioactive materials formula.
Hence, the constant 0.693 is the real number value of ln(2). Additionally, the constant 2.303 as used by convention is used to convert log value of a number x to its natural log value. Hence,. it follows that the relation which holds true is; ln(x) = 2.303 × log(x).
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The diameter of a circle is 48 meters. What is the angle measure of an arc 17 meters long?
simplest form IXL
Chana and Josiah started skating at the same time in the same direction, but Josiah had a head start 10 meters past the starting line. Chana skated 3 meters per second and Josiah skated 2 meters per second.
ANSWER:
CORRECT (SELECTED)
Josiah's distance from the starting line at a time when he is behind Chana
Point F is on line a, so it does represent Josiah's distance at a certain time. Also, point F is below line b, so it represents a distance that is less than Chana's distance.
Point F is on line a, so it does represent Josiah's distance at a certain time. Also, point F is below line b, so it represents a distance that is less than Chana's distance. This is a distance-time graph problem.
What is the proof for the above?
Recall that Josiah had a head start of 10 meters and he skates at 2 meters per second.
Since Y is the function that represents the distance in meters from the finished line, by observation, it is clear to see that all the factors that are related to his race are adequately represented in:
y = 10 + 2x
Where 10 is the head start in meters
2 is the rate at which he skates per second; and
x is the unknown amount of time in seconds.
Given that the point F sits over 25 seconds,
that is F(y) = 10 + 2 * 25
= 60 meters.
Hence, Point F is on line a, so it does represent Josiah's distance at exactly 25 seconds.
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In the diagram, line I and line m are parallel lines cut by transversal n.
b
a
n
m
The measure of both the interior angles are 70 and 110 degree.
What are Parallel Lines ?Lines they never intersect with each other and the distance between them always remains same are called parallel lines.
It is given that
Line l and m are parallel lines and are intersected by a transversal ,n
Interior angles of the same side are (2x−8) degree and (3x−7) degree
Applying the property of interior angles of parallel lines
2x -8 + 3x - 7 = 180 degree
5x -15 = 180
5x = 195
x = 39 degree
Both the angles have measure of
2 * 39 - 8 = 70 degree
3 * 39 -7 = 110 degree
Therefore the measure of both the angles are 70 and 110 degree.
The complete question is
Two parallel lines l and m are cut by a transversal n . If the interior angles of the same side of n are (2x−8) degree and (3x−7) degree , find the measure of each of these angles.
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what is w? 11w= 12 please be quick with the response.
Answer:
1.090909090909091
Step-by-step explanation:
12/11 = 1.090909090909091
W = 1.090909090909091
Answer:
w = [tex]\frac{12}{11}[/tex]
Step-by-step explanation:
11w = 12 ( isolate w by dividing both sides by 11 )
w = [tex]\frac{12}{11}[/tex]
If f(x) = x³ - 2, find f(3).
[tex]f(x) = x {}^{3} - 2 \\ f(3) = 3 {}^{3} - 2 = 27 - 2 = 25[/tex]
[tex]f(3) = 25[/tex]
x f(x)
0 24
1 12
2 6
3 3
The table represents an exponential function given by:
[tex]f(x) = 24*(1/2)^x[/tex]
Is the function exponential or quadratic?Here we have the table:
x f(x)
0 24
1 12
2 6
3 3
First, notice that for each unit that x increases, the value of f(x) decreases by its half.
This is clearly an exponential equation, whose base must be equal to (1/2).
And because when x = 0, f(0) = 24, we know that the initial value of the function is 24.
Then the exponential function is:
[tex]f(x) = 24*(1/2)^x[/tex]
Such that:
[tex]f(0) = 24*(1/2)^0 = 24\\\\f(1) = 24*(1/2)^1 = 12\\\\f(2) = 24*(1/2)^2 = 24*(1/4) = 6\\\\f(3) = 24*(1/2)^3 = 24*(1/8) = 3[/tex]
Concluding, the table represents an exponential function.
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What is the value of "y" that satisfies the expression below?
5 y + 14 = 9 ( 3 y + 1 )
Round your answer to 2 decimal points (i.e. #.##)
Answer:
0.23
Step-by-step explanation:
5y+14=27y+9
14-9=27y-5y
5=22y
dividing through by 22
y=0.23
Evaluate the fraction for x = 0. (x-1)² (1-x)² 01 0-1 02
Evaluating the given algebra fraction (x - 1)²/(1 - x)² at x = 0 gives; 1
How to Evaluate Algebra Fractions?
We want to evaluate the algebra fraction;
(x - 1)²/(1 - x)² at x = 0.
Now, let us first break down the expression to get;
[(x - 1) * (x - 1)]/[(1 - x) * (1 - x)]
At x = 0, we have;
[(0 - 1) * (0 - 1)]/[(1 - 0) * (1 - 0)]
⇒ (-1 * -1)/(1 * 1)
⇒ 1
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For a normally distributed data set with a mean of 830 and a standard deviation of 96.7, calculate the z-score for a
data point of 915.
Round this however your teacher instructs.
=================================================
Work Shown:
mu = 830 = mean
sigma = 96.7 = standard deviation
x = 915 = given raw score we want to convert
z = (x - mu)/sigma
z = (915 - 830)/(96.7)
z = (85)/(96.7)
z = 0.8790072 approximately
a. Write an ordered pair: (t, value), in which t is time from purchase and value is the current value of the car. In this case, it would be (0, Total Cash Price).
3. Find the amount of depreciation in 1 year. Determine the average rate of change (slope) in one year.
a. Write an ordered pair for the 1 - year value, which is (1, value after 1 year).
4. Find the total depreciation after 5 years.
a. Write an ordered pair for the 5 - year value, which is (5, value after 5 years).
5. Determine the following two average rates of change (slope) in the value of the car.
a. Average rate of change over 1 year
b. Average rate of change over 5 years
6. What is the practical meaning of the average rate of change over 5 years?
The value of the car decreases by $1430 per year over 5 years
The initial ordered pairThe given parameters are:
Total Cash Price: $13,7551 year depreciation: $1,811So, the ordered pair is (0, 13,755)
The amount in depreciation after 1 yearIn (a), we have:
Total Cash Price: $13,7551 year depreciation: $1,811The difference in the amounts is
Difference = 13755 - 1811
Difference = 11944
So, the ordered pair is (1, 11,944)
Total depreciation after 5 yearsWe have:
5 year depreciation = $7,150
The difference in the amounts is
Difference = 13755 - 7150
Difference = 6605
So, the ordered pair is (5, $6,605)
Average rates of changeThis is calculated as:
m = (y2 - y1)/(x2 - x1)
Over 1 year, we have:
m = (13,755-11,944)/(0-1)
m =-1811
Over 5 years, we have:
m = (13,755-6605)/(0-5)
m =-1430
The meaning of the average rate of change over 5 yearsThe average rate of change over 5 years is -1430
This means that the value of the car decreases by $1430 per year
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Missing information in the question
Total Cash Price: $13,755
1 year depreciation: $1,811
5 year depreciation: $7,150
(3-0/4a)-(10-0.8a). Solve for a
An equation is formed of two equal expressions. The value of 'a' in the given equation is 6.452.
An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The given equation can be solved for 'a' as shown below,
[tex]\dfrac{(3-0)}{4a} = (10-0.8a)\\\\\dfrac{3}{4a} = (10-0.8a)\\\\[/tex]
0.75a = 10 - 0.8a
0.75a + 0.8a = 10
1.55a = 10
a = 6.452
Hence, the value of 'a' in the given equation is 6.452.
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Find the equivalent fraction of 12/25 having a.n=60 and b.
The equivalent fraction of 12/25 is 24/50
How to determine the equivalent fraction?The fraction is given as:
Fraction = 12/25
Multiply the fraction by 1
Fraction = 12/25 * 1
Express 1 as 2/2
Fraction = 12/25 * 2/2
Evaluate the product
Fraction = 24/50
Hence, the equivalent fraction of 12/25 is 24/50
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Now, he wants to wrap it with wrapping paper. If the length of the shoebox measures 10 in, the width measures 5 in, and the height measures 3 in, how much wrapping paper does he need to cover the shoebox?
The amount of wrapping paper he need to cover the shoebox is 190 square inches
Surface area of a boxThe formula for calculating the surface area of a box is expressed as:
SA = 2(lw + wh + lh)
where
l is the length
w is the width
h is the height
Given the following parameters
l = 10in
w = 5in
h =3in
Substitute
S = 2(10*5 + 5*3 + 10*3)
S = 2(50+15+30)
S = 2(95)
S = 190 square inches
Hence the amount of wrapping paper he need to cover the shoebox is 190 square inches
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evaluate (-1 - 3²) - 4³/2
Answer:
-42
Step-by-step explanation:
You have to To subtract the fractions, then find the Least common denominator (LCD) and then combine.
pls brainliest Hope this helps have a nice day :>
[tex]\boldsymbol{(-1-3^{2})-\dfrac{4^{3} }{2} }[/tex]
Calculates 3 to the power of 2 and gets 9.
[tex]\boldsymbol{-1-9-\dfrac{4^{3} }{2} }[/tex]
Subtract 9 from −1 to get −10.
[tex]\boldsymbol{-10-\dfrac{4^{3} }{2} }[/tex]
Calculates 4 to the power of 3 and gets 64.
[tex]\boldsymbol{-10-\dfrac{64}{2} }[/tex]
Divide 64 by 2 to get 32.
[tex]\bf{-10-32 }[/tex]
Subtract 32 from −10 to get −42.
[tex]\bf{-42 \ \ \to \ \ \ Answer}[/tex]
{ Pisces04 }Renee is correct. The equations are the same when the line goes through the origin. y = mx + b is a more general form of y = mx.
If the line goes through the origin, then b = 0, so y = mx + b is y = mx + 0 or y = mx.
The equations are the same when the line goes through the origin. y = mx + b is a more general form of y = mx. Therefore, Renee is correct.
The given statement is "The equations are the same when the line goes through the origin. y = mx + b is a more general form of y = mx".
What is the origin?The point where the reference axes in a coordinate system meet. The values of coordinates are normally defined as zero.
The equation of the line is y = mx + b.
If the line goes through the origin, then b = 0, so y = mx + b is y = mx + 0 or y = mx.
The equations are the same when the line goes through the origin. y = mx + b is a more general form of y = mx. Therefore, Renee is correct.
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Pls help
Volume round to tenth
The volume of the cone to nearest tenth is 247. 12 cm ^3
How to determine the volumeNote that the shape is a cone
Volume for a cone =
[tex]\pi \: { {r}^{2} \frac{h}{3} } [/tex]
Given that radius = 5.3cm
height = 8.4cm
Substitute into the formula, we have
Volume = 3.142 × 5.3 × 5.3 × (8.4/3)
Volume = 3. 142× 28.09 × 2.8
Volume = 247. 12 cm ^3
Thus, the volume of the cone to nearest tenth is 247. 12 cm ^3
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A rectangle is removed from a right triangle to create the shaded region shown below. Find the area of the shaded region.
The area of the shaded region is 29.5 square yards.
The following calculations are to be done:
Area of the triangle:
Base of the triangle is
= 5 + 4
= 9 yard.
Height of the triangle = 6 + 5
Height of the triangle= 11 yards.
The area of the triangle is,
[tex]\ Area \ of \ the\ rectangle=\frac{1}{2} \times height\times base[/tex]
[tex]\ Area \ of \ the\ rectangle=\frac{1}{2}\times 9\times 11[/tex]
= 49.5 square yards.
What is the formula for the area of a triangle?Area of the rectangle:
[tex]=Length\times width[/tex]
[tex]=4\times 5[/tex]
= 20 square yards.
Now finally the shaded region should be
= 49.5 square yards - 20 square yards
= 29.5 square yard
Therefore we can conclude that the area of the shaded region is 29.5 square yards.
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14. Tasha is counting votes from a school election. There were 3 candidates running for treasurer, and students either voted for 1 of those 3 or they didn't vote at all. If there are 420 students in the school and half of them voted for Marcus, one- third of them voted for Mary, and one-seventh voted for Edward, how many students did not vote? (A) 10 (B) 20 (C) 42 (D) 105
Answer:
A) 10
Step-by-step explanation:
Votes for Marcus: 420/2 = 210 votes
Votes for Mary: 420/3 = 140 votes
Votes for Edward: 420/7 = 60 votes
Total number of votes: 210+140+60 = 410 votes
people who didn't vote: 420-410 = 10 people
A sub sandwich shop offers 22 toppings to choose from. How many ways could a person choose a 4-topping sandwich?
a)26
b)88
c)7,315
d) 175,500
pleaseee help, will mark branliest
There are 7,315 different combinations, thus, the correct option is c
How many combinations are there?
If we have a set of N elements, the number of different combinations of K elements (such that K ≤ N) of these N elements that we can make is:
[tex]C(N, K) = \frac{N!}{(N - K)!K!}[/tex]
In this case we have K = 4 and N = 22, replacing that, we get:
[tex]C(22, 4) = \frac{22!}{(22 - 4)!*4!} = \frac{22*21*20*19}{4*3*2*1} = 7,315[/tex]
So there are 7,315 different combinations, thus, the correct option is c.
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31) Alana ordered jeans ($28) and a sweater ($35) from a catalog. The sales tax is 8%. The shipping charges came
to $6.58. What was the total amount she was charged?
O a.) $74.62
Ob.) $77.62
Oc.) $75.62
Answer:
a) $74.62
Step-by-step explanation:
Cost of both clothes = 28+35 = $63
Tax = 0.08*63 = $5.04
Shipping: $6.54
Add: 63+5.04+6.58 = 74.62
look at this system of exquations. y=2x-1 4x +y=2 which shows a correct step using substitution to solve the system of equations?
The solution to the system of equations is x = 0.5, y = 0
How to solve the system of equations?The system of equations is given as:
y = 2x-1
4x + y=2
Substitute y = 2x-1 in 4x + y=2
4x + 2x-1 =2
Evaluate the like terms
6x = 3
Divide by 6
x = 0.5
Substitute x = 0.5 in y = 2x-1
y = 2 * 0.5 - 1
Evaluate
y = 0
Hence, the solution to the system of equations is x = 0.5, y = 0
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I NEED THE ANWERS QUICK PLS THANK YOU
Answer:
76 sqcm.
Step-by-step explanation:
2(5 x 2) + 2(5 x 4) + 2(4 x 2) = 2(10) + 2(20) + 2(8)
= 20 + 40 + 16
= 76
find the measure of the exterior angle x
The measure of the exterior angle x is 90°.
We need to find the measure of the exterior angle x.
What is the exterior angle theorem formula?An exterior angle of a triangle is equal to the sum of its two opposite non-adjacent interior angles.
Now, x°=∠A+∠B
⇒x°=30°+60°=90°
Therefore, the measure of the exterior angle x is 90°.
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Two parallel lines are cut by a transversal. What is the measure of angle 6?
[tex]\huge\boxed{\textsf{D.}\ 57^\circ}[/tex]
We know that angles 1 and 2 are supplementary angles that add up to 180 degrees.
Solve for angle 2:
[tex]\begin{aligned}\angle1+\angle2&=180^\circ\\123^\circ+\angle2&=180^\circ\\123^\circ-123^\circ+\angle2&=180^\circ-123^\circ\\\angle2&=57^\circ\end{aligned}[/tex]
We also know that angles 2 and 6 are corresponding angles, so they are equal to each other. This means that angle 6 is also 57 degrees.
For more information on this topic, search the Internet. There are many great resources on transversal lines and angles out there that expand on the few details I shared here.