The mean age (nearest year) of all the people in the office is 22.4.
How to find the mean age?Using this formula to find the mean age
Mean age = Sum of men and women age / Number of men and women
Let plug in the formula
Mean age = ( 12 women × 22 years old) + (3 men × 24 years old) / 12 women + 3 men
Mean age = 264 + 72 / 12 +3
Mean age = 336 /15
Mean age = 22.4
Therefore the mean age is 22.4.
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A cookie recipe uses 0.75 cups of sugar for every 1.25 cups of flour
How many cups of sugar will the recipe need if it uses 5 cups of
flour?
Find the interest earned on a $50,000 deposited for six years at 4 1/8% interest, compounded continuously.
The interest earned on a [tex]$\$ 50,000$[/tex] deposited for 6 years at [tex]$4\frac{1}{8 }\%$[/tex] in compounded continuously is [tex]$\$ 14040.97$[/tex].
Continuous compounding is the mathematical limit of the number of periods across which compound interest can be calculated and reinvested into the account balance. Although it is impractical, the concept of endlessly compounded interest is important in finance. This is an extreme example of compounding because most interest is compounded on a monthly, quarterly, or semiannual basis.
The given amount is [tex]$\$ 50,000$[/tex].
It will be deposited for 6 years.
With [tex]$4\frac{1}{8 }\%$[/tex] interest,
The formula for compounded continuously is
[tex]$$\begin{aligned}&A=P e^{r t} \\&P=50000 \\&r=4 \frac{1}{8}=\frac{33}{8}\end{aligned}$$[/tex]
[tex]$$\begin{aligned}r &=0.04125 \\t &=6\end{aligned}$$[/tex]
Substitute all the values
[tex]$$\begin{aligned}&A=50000 e^{0.04125 \times6} \\&A=50000 e^{0.2475} \\&A=50000\times 1.28081\\&A=64040.96811\end{aligned}$$[/tex]
[tex]$\mathrm{I}=\mathrm{A}-\mathrm{P}$[/tex]
Interest [tex]$=64040.96811-50000=14040.9681$[/tex]
Hence, Interest [tex]$=\$ 14040.97$[/tex]
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A square root function has a domain of x≥15 and a range of y≤10.
What is the range of its inverse?
y≤10
x≤15
x≥10
y≥15
Answer:
[tex] y \geq 15[/tex]
Step-by-step explanation:
The range of the inverse is the same as the domain of the original function.
Answer:y>15
Step-by-step explanation:
The zeros of the expression j2 - 4j-21 are the solutions of the equation
j²-4j-21.
j² - 4j-21 = 0
(+3_) (+5) = 0
j+ 3 = or j+ = -3
Set the expression equal to 0.
Write the equation in factored form
Use Zero Product Property.
j=7 or j = N
Solve.
The zeros of the expression j2 - 4j - 21 are 2 and .
The solutions of the quadratic equation is j = -3 and j = 7 .
In the question ,
it is given that the quadratic equation is j² - 4j - 21 = 0,
we need to find the solution of the given equation .
to find the solution , we use splitting the middle term method .
j² - 4j - 21 = 0
j² - 7j + 3j - 21 = 0 .... splitting the middle term -4j = - 7j + 3j
taking j common form first wo terms and 3 common from last two terms ,
we get
j(j - 7) +3(j - 7) = 0
(j + 3)(j - 7) = 0
j + 3 = 0 and j - 7 = 0
j = -3 and j = 7
Therefore , The solutions of the quadratic equation is j = -3 and j = 7 .
The given question is incomplete , the complete question is
Find the solutions of the quadratic equation j² - 4j - 21 = 0 ?
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If 2 is added to a number and the sum is tripled, the result is 16 more than the number. Find the number.
Using simplification, the number is −1.
Given that, If 2 is added to a number and this sum is tripled, the result is 4 more than the number.
Let the number is x.
Therefore from given information we get
2 is added to a number.
Then it is x+2.
Sum is tripled.
So 3(x+2)
4 more than number means x+4.
So according to the given statement equation should be
3(x+2)=x+4
Simplifying the expression
3x+6=x+4
Subtract 6 on both side
3x+6−6=x+4−6
3x=x−2
Subtract x on both sie
3x−x=x−2−x
2x=−2
Divide by 2 on both side we get
x=−1
Hence, the number is −1.
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decreased by 4
58
gallons in 4 minutes. What will be the change in the volume of water after 1 minute
Answer:
14.5 gallons will be gone in 1 minute
Step-by-step explanation:
just divide 58 by 4 and thats how much water will be gone in 1 minute
A vehicle is running at a constant speed on a highway. Ignore the initial acceleration at the start and final acceleration when the vehicle runs out of gasoline and comes to halt. Its gas consumption per mile is also constant. The amount of gasoline, in gallons, in the vehicle can be modeled as a linear function G ( t ) = 10 -- 2t, where t is time, in hours. Select all the true statements.le
The correct statements regarding the linear function G(t) = 10 - 2t are given as follows:
Initially, the tank has 10 gallons of gasoline.The rate of consumption is of 2 gallons per hour.The slope of G(t) represents the fuel consumption of the vehicle.The t-intercept represents the time it takes for the vehicle to run out of gas.What are the parameters of the linear function?The linear function is defined as follows:
G(t) = 10 - 2t.
In which the variables are:
G(t) is the amount of gasoline that the car has after t hours.t is the time in hours.The slope and the intercept are presented as follows:
Slope of -2: 2 gallons are consumed each hour.Intercept of 10: The initial fuel in the car is of 10 gallons.The t-intercept is:
10 - 2t = 0
2t = 10
t = 5.
Which is the time it takes for the car to run out of fuel.
Missing InformationThe options are given by the image shown at the end of the answer.
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The graph of y = f(x) is graphed below. What is the end behavior of f(x)?
The end behavior of the given graph is as x → -∞, f(x) → ∞ and as x → ∞ f(x) = ∞.
End behavior of graph
End behavior of the graph refers the behavior of the graph of f(x) as x approaches positive infinity or negative infinity. And the degree and the leading coefficient of a polynomial function will determine the end behavior of the graph.
Given,
Here we have the graph with some function as y = f(x).
Here we have to find the end behavior of the graph.
Here we can see that the value of x goes to the positive side (the right side of the graph), the graph increases upwards, and this is shown with the arrow pointing up.
So, which means that the value of x goes to ∞, then the value of y will also go to ∞.
Similarly, we can see the exact same behavior for the negative side of x (the left side of the graph), then as x goes to -∞, y will go to ∞.
Therefore, the correct option will be the second option, counting from the top.
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Is there enough information to prove the two triangles congruent? If so, write the
congruence statement and name the postulate you would use. If not, write not
possible and tell what other information you would need.
Check the picture below.
Select all of the following that are quadratic equations. 2 x2+ 12 x = 0, x2 - 2 x = 4, x + 1 x3 - 6 x2 + 8 = 0, 5 x - 3 = 0, 5 x - 1 = 3x + 8, 9 x2 + 6 x - 3 = 0
2x²+12x=0 , x²-2x=4 and 9x²+6x-3=0 are Quadratic equation
Quadratic equations are polynomial equations whose degree is of 2 in one of the variable.
The standard form of quadratic equation is ax²+bx+c = d where a, b and c are real numbers and a ≠ 0.
In general form of quadratic equation , "a" is known as leading coefficient and "c" is known as absolute term of function.
In the given question,
Equation whose max. degree will be 2 will be quadratic .
2x²+12x=0 , equation is quadratic as degree of equation is 2
x²-2x=4 , equation is quadratic as degree of equation is 2
x³-6x²+8=0 , Degree of equation is 3
Therefore , equation is not quadratic
5x-3=0 , Degree of equation is 1
Therefore , equation is not quadratic
5x-1=3x+8 , Degree of equation is 1
Therefore , equation is not quadratic
9x²+6x-3=0 , Degree of equation is 2
It is quadratic equation.
Hence , 2x²+12x=0 , x²-2x=4 and 9x²+6x-3=0 are quadratic equation
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can somebody please help me
Answer: D
Step-by-step explanation: I believe this the correct answer. If you start by looking at the "right 3 units", going right on a coordinate plane is - and left is +, so right 3 units is -3. Then, down 4 units is -4 (on coordinate plane, up is + and down is -).
So then, plug it into the equation: h(x)= {x-3}-4
I hope this helps and you get it right :)
The light in a lighthouse flashes every 20 seconds.
How many times will it flash in one hour?
Answer:
180 flashes
Step-by-step explanation:
The lighthouse flashes 3 times in a minute then multiplied by 60 which is 180 flashes.
NASA launches a rocket at t = 0 seconds. Its position (height), in meters above sea-level, as a function
time, t, is given by s(t): - 4.9t2 + 187t + 192. Use this position function to answer the following
questions. Round solutions to three decimal places, if necessary.
The rocket splashes down after 39.164 seconds. The rocket reach its peak height 19.081 seconds after launch. The rocket peaks at 1976.13 meters above sea level.
The function of height is given by,
h(t) = -4.9t² + 187t + 192
Once the rocket will be splashed down in sea, means the height of the rocket will be zero. Means
x h(t) = 0
-4.9t² + 187t + 192 = 0
Solving the quadratic equation with quadratic formula, we have two values of t
t = 39.164 and t = -1.001
We will consider the positive value of the time
So the answer is 39.164 seconds.
For getting the maximum value, we should differentiate the function of height and make it equal to zero.
[tex]\frac{dh(t)}{dt} = \frac{d}{dt} (-4.9t^2 + 187 t + 192)[/tex]
For maximum value of h, [tex]\frac{dh (t)}{dt} = 0[/tex]
0 = -4.9 × (2t) + 187
t = 19.081 seconds
At this time, the height of rocket will be maximum.
So putting the vaiue in the given function.
h = -4.9 × (19.081)² + 187 (19.081) + 192
h = 1976.13 meters
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Solve the system if possible by using Cramer's rule. If Cramer's rule does not apply, solve the system by using another method. Write all numbers as integers or
simplified fractions.
-4x-5y+6z = 5
-3x+6y-2z = 4
5x+9y-3z = 1
The solution of the system using Cramer's Rule is x= -0.53, y=0.78 and z=1.13.
In the given question we have to solve the system using the Cramer's rule.
The given equations are
-4x-5y+6z = 5
-3x+6y-2z = 4
5x+9y-3z = 1
From the Cramer's rule
[tex]\left[\begin{array}{ccc}-4&-5&6\\-3&6&-2\\5&9&-3\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}5\\4\\1\end{array}\right][/tex]
Here,
A = [tex]\left[\begin{array}{ccc}-4&-5&6\\-3&6&-2\\5&9&-3\end{array}\right][/tex]
X= [tex]\left[\begin{array}{ccc}x\\y\\z\end{array}\right][/tex]
B = [tex]\left[\begin{array}{ccc}5\\4\\1\end{array}\right][/tex]
Now D=|A|
D= [tex]\left|\begin{array}{ccc}-4&-5&6\\-3&6&-2\\5&9&-3\end{array}\right|[/tex]
D= [tex]-4\left|\begin{array}{ccc}6&-2\\9&-3\end{array}\right|-(-5)\left|\begin{array}{ccc}-3&-2\\5&-3\end{array}\right|+6\left|\begin{array}{ccc}-3&6\\5&9\end{array}\right|[/tex]
D= -4[6×(-3)-(-2)×9]+5[(-3)×(-3)-(-2)×5]+6[(-3)×9-5×6]
D= -4[-18+18]+5[9+10]+6[-27-30]
D= -4×0+5×19+6×(-57)
D= 0+95-342
D= -247
[tex]D_{x}=\left[\begin{array}{ccc}5&-5&6\\4&6&-2\\1&9&-3\end{array}\right][/tex]
Simplifying the matrix
[tex]D_{x}=5\left|\begin{array}{ccc}6&-2\\9&-3\end{array}\right|-(-5)\left|\begin{array}{ccc}4&-2\\1&-3\end{array}\right|+6\left|\begin{array}{ccc}4&6\\1&9\end{array}\right|[/tex]
[tex]D_{x}[/tex] = 5[6×(-3)-(-2)×9]+5[4×(-3)-(-2)×1]+6[4×9-1×6]
[tex]D_{x}[/tex] = 5[-18+18]+5[-12+2]+6[36-6]
[tex]D_{x}[/tex] = 5×0+5×(-10)+6×30
[tex]D_{x}[/tex] = 0-50+180
[tex]D_{x}[/tex] = 130
[tex]D_{y}=\left[\begin{array}{ccc}-4&5&6\\-3&4&-2\\5&1&-3\end{array}\right][/tex]
Simplifying the matrix
[tex]D_{y}= -4\left|\begin{array}{ccc}4&-2\\1&-3\end{array}\right|-5\left|\begin{array}{ccc}-3&-2\\5&-3\end{array}\right|+6\left|\begin{array}{ccc}-3&4\\5&1\end{array}\right|[/tex]
[tex]D_{y}[/tex] = -4[4×(-3)-(-2)×1]-5[(-3)×(-3)-(-2)×5]+6[(-3)×1-4×5]
[tex]D_{y}[/tex] = -4[-12+2]-5[9+10]+6[-3-20]
[tex]D_{y}[/tex] = (-4)×(-10)-5×19+6×(-23)
[tex]D_{y}[/tex] = 40-95-138
[tex]D_{y}[/tex] = -193
[tex]D_{z}=\left[\begin{array}{ccc}-4&-5&5\\-3&6&4\\5&9&1\end{array}\right][/tex]
Simplifying the matrix
[tex]D_{z}=-4\left|\begin{array}{ccc}6&4\\9&1\end{array}\right|-(-5)\left|\begin{array}{ccc}-3&4\\5&1\end{array}\right|+5\left|\begin{array}{ccc}-3&6\\5&9\end{array}\right|[/tex]
[tex]D_{z}[/tex] = -4[6×1-4×9]+5[1×(-3)-4×5]+5[(-3)×9-5×6]
[tex]D_{z}[/tex] = -4[6-36]+5[-3-20]+5[-27-30]
[tex]D_{z}[/tex] = (-4)×(-30)+5×(-23)+5×(-57)
[tex]D_{z}[/tex] = 120-115-285
[tex]D_{z}[/tex] = -280
As we know that; x=Dx/D, y=Dy/D, z=Dz/D
x=130/(-247)
x= -0.53
y=(-193)/(-247)
y=0.78
z=(-280)/(-247)
z=1.13
Hence, the solution of the system using Cramer's Rule is x= -0.53, y=0.78 and z=1.13.
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18) In the Pie Chart Example below, the city of Miami is trying to determine how many new visitors visit their beaches each month in the summer. If the total number of visitors in the entire summer is 300,000 how many visitors come in June? A. 30,000 B. 60,000 C. 135,000 D. 72,000
The number of visitors to the beach in June is B. 60000.
How to calculate the value?Since the pie chart isn't given, let the assumed percentage for the visit to the beach in June be 20%.
In this case, the new visitors visit their beaches each month in the summer. If the total number of visitors in the entire summer is 300,000 will be:
= Percentage for visits × Total people
= 20% × 300000
= 60000
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The table shows the height of water in a pool as it is being filled. A table showing Height of Water in a Pool with two columns and six rows. The first column, Time in minutes, has the entries, 2, 4, 6, 8, 10. The second column, Height in inches, has the entries, 8, 12, 16, 20, 24. The slope of the line through the points is 2. Which statement describes how the slope relates to the height of the water in the pool? The height of the water increases 2 inches per minute. The height of the water decreases 2 inches per minute. The height of the water was 2 inches before any water was added. The height of the water will be 2 inches when the pool is filled.
The most appropriate interpretation for the slope of the data given is the height of water in the pool increases by 2 inches per minute. Option (1) is correct.
The slope of a line, also known as its gradient, is the value of the steepness or direction of a line in a coordinate plane. Slope can be calculated using various methods given a line equation or the coordinates of points on a straight line.
Given that
Time Height
2 8
4 12
6 16
8 20
10 24
The slope of the line = 2
A line's slope is also known as its gradient or rate of change.
The slope can be positive or negative; positive slope values indicate an increase in x as y increases and vice versa.
A negative slope indicates that one variable decreases as the other increases.
Because the slope value given here is positive, we can conclude that the height of the water increases over time.
As a result, the height of the water rises by 2 inches per minute.
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Find slope of line please no links
Answer:
Step-by-step explanation:
Using
Point A: x= 1 and y=3
And point B: x=-2 and y=-6
use equation of slope and substitute the values
Slope= YB-YA/Xb-Xa
= -6-3/-2-1
=3
How do I solve this problem step-by-step? 5(7+6)x9+2
Answer:587
Step-by-step explanation: multiply 5 by 7 and 6,thatll give you 30+35=65
then 65 multiplied by 9 is 585 then add2 is 587
Solve the system of equations by graphing.
x-y=-4
x+y=8
The given quadrilateral ABCD is an isosceles trapezoid. Which choice is NOT true about ABCD?
A) 2x + 10 = 4x - 30
B) angle A+ angle B+ angle C+ angle D=180^
C) angle A+ angle B+ angle C+ angle D=360^
D) AR = CD
Answer: B
Step-by-step explanation:
What is an isosceles trapezoid?
An isosceles trapezoid is a type of quadrilateral in which the non-parallel sides have equal length and angle measure.
Let's address each answer to see which are true:
A) True: By definition of an isosceles trapezoid, the non-parallel sides have equal length and angle measure. 2x+10 and 4x-30 are written as equations to represent the unknown measurement of the angles A and D. Because this is an isosceles trapezoid, these angles would have the same measurement, meaning they are equal to each other.
B) False: A trapezoid is a quadrilateral. Quadrilaterals are four-sided figures which angles add up to 360°. Some other shapes that are quadrilaterals are squares, rectangles rhombuses and trapezoids. Because a trapezoid is a quadrilateral, the angles do not and can not add up to 180°
C) True: A trapezoid is a quadrilateral, which is a shape which angles add up to 360°. This means that Angles A, B, C, D of this shape should also add up to 360°.
D) True: An isosceles trapezoid is a type of trapezoid whose non-parallel sides have equal side lengths and angles measurements. Due to this definition, AB and CD would have the same length.
A toaster oven usually sells for $60. If the toaster oven is 20% off, and sales tax is 7%, what is the total price of the toaster oven, including tax?
The total price of the toaster oven, including tax is $51.36.
How to calculate the value?Given that the toaster oven usually sells for $60 and the toaster oven is 20% off, the new price will be;
= Normal price - Discount
= $60 - (20% × $60)
= $60 - $12
= $48
Also, sales tax is 7%, therefore the new price will be:
= $48 + (7% × $48)
= $48 + $3.36
= $51.36
The price is $51.36.
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Salespeople at a certain company have a quota to meet each month. On average, they hit the quota 68% of the
time. If a salesperson hits the quota, the probability of being promoted in the next six months is 0.41. If a person
doesn't hit the quota, the probability of being promoted is 0.14.
Use the tree diagram to complete each statement.
The probability of no promotion, given that a salesperson hit the quota: A is
The probability of a promotion, given that a salesperson missed the quota: B is
The probability of no promotion, given that a salesperson missed the quota: C is
The probability that a salesperson hit the quota and got promoted: D is
V
Done
The probability that a salesperson hit the quota, given that the salesperson was promoted, using the tree diagram,: is option c 0.86
What is a probability?
The probability of an event in an experiment is calculated by the division of the number of desired outcomes by the number of total outcomes in the experiment.
From the tree diagram, there are two ways to obtain the promotion:
0.41 of 0.68 (hit the quota).
0.14 of 0.32 (did not hit the quota).
Hence the probability of getting a promotion is:
P(A) = 0.41 x 0.68 + 0.14 x 0.32 = 0.3236.
The probability of both getting a promotion and hitting the quota is:
P(A and B) = 0.41 x 0.68 = 0.2788.
Hence the conditional probability is:
P(B|A) = P(A and B)/P(A) = 0.2788/0.3236 = 0.86. (approximately).
The probability that a salesperson hit the quota, given that the salesperson was promoted, using the tree diagram,: is option c 0.86
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Find the value of each variable 5x-7
Answer:
-35
Step-by-step explanation:
The legend on a map states that
1 inch is 500 miles. If you measure
8 inches on the map, how many
miles would the actual distance be?
The actual distance will be 4000 miles.
According to the question,
We have the following information:
The legend on a map states that 1 inch is 500 miles.
So, this statement can be rewritten in the form of following expression:
1 inch = 500 miles
Now, in order to find the actual distance for 8 inches, we will multiply the distance in 1 inch with 8.
(More to know: measurements like this are used in daily life to find the actual distance between two places.)
So, we have the following expression:
8 inches = 500*8 miles
8 inches = 4000 miles
Hence, the actual distance will be 4000 miles if it measures 8 inches on the map.
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y’all can help me with this one pleaseI need to write an equation for each line
The equation of the line m is y = -2x + 4, for n is y = x - 1, for p is x = -4, and for l is y = 4.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
The graph on which the straight line is shown:
The equation of the line m
(2, 0) and (0, 4)
y = (4)/(-2)[x - 2]
y = -2(x - 2)
y = -2x + 4
The equation the line n:
(1, 0) and (0, -1)
y = (-1)/(-1)[x - 1]
y = x - 1
The equation of the line p:
x = -4
The equation of the line l:
y = 4
Thus, the equation of the line m is y = -2x + 4, for n, is y = x - 1, for p is x = -4, and for l is y = 4.
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Which relationship has a zero slope? A two column table with five rows. The first column, x, has the entries, negative 3, negative 1, 1, 3. The second column, y, has the entries, 2, 2, 2, 2. A two column table with five rows. The first column, x, has the entries, negative 3, negative 1, 1, 3. The second column, y, has the entries, 3, 1, negative 1, negative 3. A coordinate plane with a straight line starting at (negative 5, negative 5) and passing through the origin, and ending at (5, 5) A coordinate plane with a straight line starting iat (negative 2, 5) and passing the x-axis at (negative 2, 0), and ending at (negative 2, 5).
The relationship which has a zero slope is a two column table with five rows. The first column, x, has the entries, negative 3, negative 1, 1, 3, and the second column, y, has the entries, 2, 2, 2, 2. Option A is correct.
We know that a line has a zero slope is when the line is parallel to the x-axis.
The slope of a line is given by;
m = (y₂ - y₁) / (x₂ - x₁)
where (x₂, y₂) and (x₁, y₁) are the coordinates of any two points on the line of slope.
For option A:
The given coordinates are;
(-3, 2), (-1, 2), (1, 2), (3, 2)
Choose any two points to calculate the slope of the line.
We will choose the first two points and put the values in the above formula, we will get;
m = (2 - 2) / (-1 (-3)) = 0 / 2 = 0
So, the slope of the line is 0.
Thus, the relationship which has a zero slope is a two column table with five rows. The first column, x, has the entries, negative 3, negative 1, 1, 3, and the second column, y, has the entries, 2, 2, 2, 2. Option A is correct.
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Which fraction is greater of 8/400 or 8/10
Newton earns $195 for
working 15 hours as a radio host. How
much money does Newton earn in
3 hours?
Newton earns $39 for working 3 hours as a radio host.
What is meant by time and work?In terms of time and work, it refers to how long it takes a person or group of individuals to perform a task and how well each of them does it. A crucial concept that time and labour have in common with other arithmetic topics is the concept of proportionality. Efficiency is inversely proportional to time required while the amount of work is constant.
Efficiency serves as the proportionality constant, and work and time are directly proportional.
Given,
As a radio host, Newton puts in 15 hours and makes $195..
For a one hour the employee earns $13
So with this information we can put:
13×3=39
In 3 hours Newton earns $39 for working as a radio host.
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In ΔJKL, m∠J = 67° and m∠L = 90°. Determine the measure of the exterior angle to ∠K.
23°
113°
157°
78.5°
Answer:
[tex]157^{\circ}[/tex]
Step-by-step explanation:
Using the exterior angle theorem,
[tex]m\angle K=m\angle J+m\angle L=157^{\circ}[/tex]
Two angles whose sum is 180° are supplementary angles. find the measure of the supplementary angle shown in the figure
Step-by-step explanation:
together they are 180°.
so,
(11x + 2) + (8x + 7) = 180
11x + 2 + 8x + 7 = 180
19x + 9 = 180
19x = 171
x = 171/19 = 9
and the angles are
(11x + 2) = 11×9 + 2 = 99 + 2 = 101°
(8x + 7) = 8×9 + 7 = 72 + 7 = 79°