Answer:
0.0369
Step-by-step explanation:
normalcdf (1220,1320,900,200) is 0.0369
Goal
Your task is to create a monthly budget given certain circumstances.
Role
You are a single person who just received a full-time job in a factory (40 hours). You will make $12.00 an hour.
Audience
You need to convince your parents that you can maintain a budget to live in a one-bedroom apartment that costs $300 for rent a month.
Situation
The challenge involves dealing with finding average heating, water, sewage bills in your area so that you can include those in your budget.
Product, Performance, and Purpose
You need to develop a monthly budget so that you can show your parents that you can afford the expenses.
Please upload your completed assignment here. Be sure you have included your name at the top of your document and as part of the file name.
The development of the personal budget that convinces parents that one can maintain an independent living is detailed as follows using the 50: 30: 20 rule:
50% for necessities (housing, food, transportation, utilities) $740
30% for luxuries, savings, vacations, entertainment, etc. $461
20% for Emergency Funds and Retirement $335
What is a personal budget?A personal budget is the household budget for a single person for a period.
The personal budget shows an estimate of the person's revenue and expenses over the period.
Data and Calculations:Hourly rate of earnings = $12
Working hours per week = 40 hours
Working hours per month = 160 hours (40 x 4 weeks)
Total monthly earnings = $1,920 ($12 x 160)
Assumed tax rate = 20%
After-tax take-home pay = $1,536 ($1,920 x 1 - 20%)
Monthly Necessities:Rent of apartment = $300
Heating = $40
Water cost = $20
Sewage bill = $10
Food = $300
Transportation = $50
Other costs = $20
Total cost for necessities = $740
Thus, the development of the personal budget shows that one can maintain an independent living from the parents as a single person.
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What is angle Data please help
Answer:
C. 74°
Step-by-step explanation:
Cosine Rule (for finding angles)
[tex]\sf \cos(C)=\dfrac{a^2+b^2-c^2}{2ab}[/tex]
where:
C = anglea and b = sides adjacent the anglec = side opposite the angleGiven:
C = [tex]\theta[/tex]a = 5b = 11c = [tex]\sf \sqrt{115}[/tex]Substitute these values into the formula:
[tex]\implies \sf \cos(\theta)=\dfrac{5^2+11^2-(\sqrt{115})^2}{2(5)(11)}[/tex]
[tex]\implies \sf \cos(\theta)=\dfrac{25+121-115}{110}[/tex]
[tex]\implies \sf \cos(\theta)=\dfrac{31}{110}[/tex]
[tex]\implies \sf \theta=\cos^{-1}\left(\dfrac{31}{110}\right)[/tex]
[tex]\implies \sf \theta=74^{\circ} \quad (nearest\:degree)[/tex]
Which one is the right conversion?
Answer:
1, 4, 5, 6
Step-by-step explanation:
to convert a rational to an exponential it's the index (number left of radical) over the power (number on the right).
you can also double check by plugging both into a calculator and see if they equal the same number.
Select the correct answer from each drop-down menu. y = f(x) = (1/2) ^ 5 Consider the function The value of f(- 7) is The value of f(5) rounded to the nearest ten thousandth, is
The values of the functions are:
1. y = f(-7) = 128
2. y = f(5) = 0.0313
How to Find the Value of a Function?We can evaluate a function by substituting the given value into the equation of the function, then simplify.
Given the function, y = f(x) = (1/2) ^ x
1. Find the value of f(-7):
y = f(-7) = (1/2)^-7
y = f(-7) = 2^7
y = f(-7) = 128
2. 1. Find the value of f(5):
y = f(5) = (1/2)^5
y = f(5) = 0.0313
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1. Ms. Cedric bought a jar for 25 dimes. If she had 75
nickels, how much money is left in her bag?
4.
Solve the system of inequalities graphically. Label the solution set with an S.
Help asap
Answer:
Step-by-step explanation:
The physician prescribed penicillin 250 mg. The bottle from the supply cabinet is labeled, "Penicillin 500 mg per cc." The correct amount to administer would be CC.
Select one:
A. 0.5
B. 5.0
C. 0.25
D. 0.75
Using proportions, it is found that the correct amount to administer of CC would be of:
A. 0.5.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, 500 mg are equivalent to one cc. How many cc are equivalent to 250 mg? Hence the rule of three is given by:
500 mg - 1 cc
250 mg - x cc
Applying cross multiplication:
500x = 250
c = 0.5.
Hence option A is correct.
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The shorter leg of a right triangle is 5 inches shorter than the longer leg. The hypotenuse is 5 inches longer than the longer leg. Find the side lengths of the triangle.
Answer:
longer leg: 20 in
shorter leg: 15 in
hypotenuse: 25 in
Formulas:
Pythagorean Theorem
[tex]c^2 = a^2 + b^2[/tex]
c ... hypotenuse
a ... one leg
b ... another leg
Pythagorean theorem is used in right triangles (triangles in which one angle is 90°).
Step-by-step explanation:
longer leg: x
shorter leg: x - 5
hypotenuse: x + 5
To find x (longer leg), let's use Pythagorean theorem.
[tex]c^2 = a^2 + b^2\\(x+5)^2 = x^2 + (x-5)^2\\x^2 + 10x + 25= x^2 + x^2 -10x + 25\\x^2 + 10x = 2x^2 - 10x\\0 = x^2 - 20x[/tex]
Now let's factorize to get solutions for x.
[tex]0 = x(x-20)[/tex]
First solution:
[tex]x = 0[/tex]
Second solution:
[tex]x - 20 = 0\\x = 20[/tex]
Since a side of a triangle has to be a positive number, x is equal to 20.
Now let's just substitute x back to get side lengths. From the question the lengths are in inches.
longer leg: x = 20 in
shorter leg: x - 5 = 20 - 5 = 15 in
hypotenuse: x + 5 = 20 + 5 = 25 in
Determine if the function is an even function, an odd function or neither. > = −6x² – 5x² −2 even neither odd
Answer: even
Step-by-step explanation:
A function is even if f(x)=f(-x), and odd if f(x)=-f(-x). If a function satisfies neither of these, it is neither even nor odd.
[tex]f(x)_=-6x^{2}-5x^{2}-2=-11x^{2}-2\\\\f(-x)=-11(-x)^{2}-2=-11x^{2}-2\\\\\therefore f(x)=f(-x)[/tex]
Therefore, the function is even.
The members of a club decide to sell hats to raise money. They originally
planned to charge $12 for a hat, but they reduced that price by $2. They sold
41 hats at the reduced price.
Select the expression representing the amount of money earned.
OA. 41(12-2)
OB. 41(12+2)
OC. 41(12) +2
OD. 41(12) - 2
Answer:
A. 41 (12 - 2)
Step-by-step explanation:
If the club decided to charge $12 for a hat, but reduced the price by $2, the reduced price of the hat is (12 - 2). The amount of money earned is based upon the price of the hat multiplied by the number of hats sold. Therefore, the answer is 41 (12 - 2).
Hope this helped :)
Please help! I don’t think my answers are correct. Photo is attached.
Answer:
Step-by-step explanation:
(a). In set notation:
B. { x | x < 2 }
(b).
( - ∞ , 2 )
(c). See attachment.
If-5x + 4y = -3 is a true equation, what would be the value of
-6(-5x+4y)?
Answer:
Step-by-step explanation:
-5x+4y=-3
-6(-5x+4y)=-6×(-3)=18
i needs help with it please
Answer:
(i) (0, -32)
(ii) (-4, 0) and (8, 0)
(iii) x = 2
(iv) (2, -36)
(v) (2, -36) minimum
Step-by-step explanation:
Given quadratic equation:
[tex]y=x^2-4x-32[/tex]
Part (i)
The y-intercept is the point at which the curve crosses the y-axis.
To find the y-intercept, substitute x = 0 into the given equation:
[tex]\implies (0)^2-4(0)-32=-32[/tex]
Therefore, the y-intercept is at (0, -32)
Part (ii)
The zeros are the points at which the curve crosses the x-axis.
To find the zeros, substitute y = 0 into the given equation and factor:
[tex]\implies x^2-4x-32=0[/tex]
[tex]\implies x^2-8x+4x-32=0[/tex]
[tex]\implies x(x-8)+4(x-8)=0[/tex]
[tex]\implies (x+4)(x-8)=0[/tex]
Therefore:
[tex](x+4)=0 \implies x=-4[/tex]
[tex](x-8)=0 \implies x=8[/tex]
So the zeros are (-4, 0) and (8, 0)
Part (iii)
The axis of symmetry is a vertical straight line that divides the curve into two symmetrical parts. The axis of symmetry is the x-value of the mid-point of the zeros.
[tex]\sf \implies midpoint=\dfrac{8+(-4)}{2}=2[/tex]
Therefore, the axis of symmetry is: x = 2
Part (iv)
The vertex is the turning point of the parabola.
If the leading coefficient is positive, the parabola opens upwards and the vertex is the minimum point.
If the leading coefficient is negative, the parabola opens downwards and the vertex is the maximum point.
The axis of symmetry is the x-value of the vertex.
To find the y-value, substitute x = 2 into the equation:
[tex]\implies (2)^2-4(2)-32=-36[/tex]
Therefore, the vertex is (2, -36)
Part (v)
The optimal value is also known as the vertex.
Therefore, the optimal value is (2, -36).
As the leading coefficient of the given quadratic equation is positive, the parabola opens upwards and so the optimal value is a minimum.
Solve 8x+5y=2 and y-2=0.Also verify thmm....
Answer:
Solution: Here, the given equations are,
[tex]: \implies8x+5y=2...(i)\:and\:y-2=0...(ii)[/tex]
From equation,(ii); y-2=0
[tex] \therefore \: y = 2.........(iii)[/tex]
Substituting the value of y from equation (iii) to equation (i),we get
[tex]: \implies{8x + 5y = 2}[/tex]
[tex]: \implies{8x + 5(2) = 2}[/tex]
[tex]: \implies{8x = 2 - 10}[/tex]
[tex]: \implies{8x = - 8}[/tex]
[tex]: \implies{x = - 1}[/tex]
[tex] \therefore \: x = - 1[/tex]
Thus, x= -1 and y= 2 is the solution.
Checking at (-1,2)8x+5y=2...(i) y-2=0...(ii)
8(-1)+5(2)=2 2-2=0
2=2(True) 0=0(True)
Substratum is an open-source network that allows anyone to allocate spare computing resources to support the foundation of the decentralized web. SUB is the cryptocurrency that supports this network. On the 10th of January 2018, the price of SUB was $2.88 and on the 5th of April 2019 the price was $0.02. When rounded to one decimal place, which of the below gives the percentage decrease of the price of SUB from the 10th of Jan 2018 to the 5th of April 2019?
The percentage decrease will be equal to 99.30 %.
What are percentages?The Percentage is defined as representing any number with respect to the 100. It is denoted by the sign %.
Given that:-
SUB is the cryptocurrency that supports this network. On the 10th of January 2018, the price of SUB was $2.88 and on the 5th of April 2019 the price was $0.02The percentage decrease will be calculated as:-
Percentage decrease = [tex]\dfrac{2.88 - 0.02}{2.88}[/tex]
Percentage decrease = 0.9930 = 99.30%
Therefore the percentage decrease will be equal to 99.30 %.
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The length of a new rectangular playing field is 4 yards longer than quadruple the width. If the perimeter of the rectangular playing field is 558 yards, what are its dimensions?
The width is yards.
Answer:
55 x 224 yards
Step-by-step explanation:
w + w + 2 * ( 4 + 4w) = 558 (given)
10 w + 8 =558
w = 55 then L = 4 + 4w = 224 yards
Consider the given system of linear equations. 2x+y-z=8 x+4y+z=7 -3x+2y-3z=21
The system of equations has the solution:
x = 111/42
y = 27/14
z = -15/6
How to solve the system of linear equations?We start with 3 linear equations:
2x+y-z=8
x+4y+z=7
-3x+2y-3z=21
To solve this, first we need to isolate one of the variables. I will isolate x on the second one:
x = 7 - 4y - z
Now we can replace that in the other two:
2*( 7 - 4y - z) + y - z = 8
-3*(7 - 4y - z) + 2y - 3z = 21
Now we need to isolate other variable, let's isolate y on the above one:
14 - 8y - 2z + y - z = 8
-7y - 3z = 8 - 14 = -6
z = (-6 + 7y)/-3 = 2 - (7/3)*y
Now we replace this on the last equation:
-21 + 12y -3z + 2y - 3z = 21
14y - 6z = 42
14y - 6*(2 - (7/3)*y) = 42
14y - 12 + 14y = 42
28y = 42 + 12 = 54
y = 54/28 = 27/14
Now that we know the value of y, we can find the value of z:
z = 2 - (7/3)*y = 2 - (7/3)*27/14 = 2 - 27/6 = -15/6
And the value of x:
x = 7 - 4y - z = 7 - 4*(27/14) + 15/6 = 7 - 48/7 + 15/6 = 111/42
So the solution is:
x = 111/42
y = 27/14
z = -15/6
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Given that these simultaneous equations
x-y=k
2x²+y²-15
have exactly one pair of solutions, find k.
The answer is supposedly (±3√10)/2, but I don't know how to get to the answer
The value of k is[tex](3\sqrt{ 10})/2[/tex]
How to solve the simultaneous equation?Given:
x-y=k.............(eq i)
2x²+y²-15..............(eq ii)
We would make y the subject formula in eq ii
2x²+y²-15= 0
2x² + y²= 15
y²= 15-2x²
y= [tex]\sqrt{15-2x^2}[/tex]...........(eq iii)
Substitute the value of y into eq i
x-([tex]\sqrt{15-2x^2}[/tex]= k
x- ([tex]\sqrt{15} - 2x[/tex]= k
k= [tex](3\sqrt{ 10})/2[/tex]
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Find the height of a trapezium below with are 90cm and parallel sides 6 and 19.
Answer:
7.2 cm
Step-by-step explanation:
The height of the trapezium can be found by making use of the area formula with known values filled in.
__
solve for heightThe area of a trapezium is given by ...
A = 1/2(b1 +b2)h . . . . b1, b2 are the parallel sides, h is the height
Using the given values, we have ...
90 cm² = 1/2(6 cm +19 cm)h . . . . . . use the known values
(90 cm²)/(12.5 cm) = h = 7.2 cm . . . . divide by the coefficient of h
The height of the trapezium is 7.2 cm.
Ian buys 4 bananas and 2 apples. Each banana has a mass of 120 grams. Each apple has a mass of 180 grams.
Which is the total mass of the fruit that Ian buys?
A.
300 grams
B.
580 grams
C.
840 grams
D.
960 grams
Answer:
THE ANSWER IS A CORRECT ME IF I WRONG
Please help we’re stuck
Answer:
Divide 12 by -6
1. Find the equation of a normal to the curve y= 2² - 2x +3 at the point (3,0)
I think you meant to say the equation is
y = 2x² - 2x + 3
Differentiate both sides with respect to x :
dy/dx = 4x - 2
At the point (3, 0), the slope of the tangent line is dy/dx(3) = 4•3 - 2 = 10. Then the normal line to the curve at (3, 0) has slope -1/10.
Using the point-slope formula, the equation of the normal line is
y - 0 = -1/10 (x - 3) ⇒ y = (3 - x)/10
what are the amounts of interest and maturity value of a loan for 25,000 at 12% simple interest for 5 years
Answer:
Interest= 15,000
Maturity Value=40,000
Step-by-step explanation:
Simple Interest
V= (principal) * (rate) * (# of periods)
=(25,000)*(0.12)*(5)
=15,000
Maturity Value
V= P*(1+rt)
=25,000*(1+(.12)(5))First, converting R percent to r a decimal
r = R/100 = 12%/100 = 0.12 per year.
Solving our equation:
V = 25000(1 + (0.12 × 5)) = 40000
V = 40,000.00
hope it will help you
thank u
Identify the composition that is represented by: r (90, 0) T(−2,4)
A translation left 2, up 4 and then a reflection of 90°
A rotation of 90° and then a translation left 2, up 4.
A translation of left 2, up 4 and then a rotation of 90°.
A reflection of 90° and then a translation left 2, up 4.
The composition of the transformation is (b) A rotation of 90° and then a translation left 2, up 4.
How to determine the transformation?The transformation rule is given as:
r (90, 0) T(−2,4)
The r(90,0) represents a rotation of 90 degrees.
The other part of the transformation rule can be rewritten as:
T(-2,4) => (x - 2,y + 4)
This means a translation right by 2 units and up by 4 units
Hence, the composition of the transformation is (b)
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Answer: left 2
Step-by-step explanation:
an airplane has an airspeed of 530 kilometers per hour bearing N45 degrees E. The wind velocity is 30 kilometers per hour in the direction N30 degrees W. Find the resultant vector representing the path of the plane relative to the ground. What is the ground speed of the plane? What is its direction?
For an airplane has an airspeed of 530 kilometers per hour bearing N45 degrees E, the ground speed of the plane and its direction is mathematically given as
Vg=556.10km/hr[tex]\theta=52.99East[/tex]What is the ground speed of the plane and its direction?Generally, the equation for the velocity of the plane is mathematically given as
[tex]Vp=Fcos\thetai+Fsin\theta j[/tex]
Therefore
Vp=530cos45i+530sin45j
Vp= 374.76i+374.76j
For wind speed
Vm=80cos(90+30)i+80sin(90+30)j
Vm=-40i+69.28j
Hence, there resultant is
Vr=Vm +Vp
Vr=374.76i+374.76j + 40i+69.28j
Vr=334.77i+1444.05j
In conclusion, the Ground speed is
[tex]Vg=\sqrt{334.77^2+1444.05^2}[/tex]
Vg=556.10km/hr
Direction
[tex]Tan \theta=\frac{444.05}{334.77}[/tex]
[tex]\theta=52.99East[/tex]
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The half-life of cobalt-60 (used in
radiation therapy) is 5.26 years (actual
data). How much of a 200 g sample of
cobalt-60 will remain after 26.3 years?
Answer:
6.25 gm left
Step-by-step explanation:
Find the number of half lives in 26.3 years
26.3 / 5.26 = 5 half lives
(1/2) ^5 = 1/32 nd of the original will be left
1/32 * 200g = 6.25 gm left
Los disminuyentes de liquido normal en ula persona sana es de 0.6mL/kg/hr. Sabiendo que don pedro cuenta con 39 grados de fiebre y pesa82 kg. Calcule la perdida de liquido/h
The question requires the computation of loss body fluid. The results show that Don Pedro's loss of body fluid per hour is 54,234ml/hours. See computation below.
What is the loss of body fluid?This refer to the rate at which a human being loses water on the hour. The formula for this is given as:
The Body weight in lb x percentage rate of dehydration (given in decimal form) x 500.
Hence, Don Pedro's loss of fluid per house is:
82 x 0.6 x 500;
Recall that in the formula, the weight is given in lb. So we convert Pedro's weight to Lb.
1kg = 2.20462Lb
Hence
80kg = 80 * 2.20462 = 176.37
Hence
Pedro's loss of fluid per house =
180.779 x 0.6 x 500
= 54,233.70
≈ 54, 234 ml/h
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Denise bikes 3 miles to her friend's house, and then she bikes home. The average rate biking to her friend's house is twice the average rate coming home. Write and simplify an expression for the time it takes Denise to make a round-trip in terms of the average rate coming home x.
Hint : Use d = rt.
The total time for the trip is:
T = 3mi*( 3/2x).
Where x is the rate at which she comes home.
How to find the time for the total trip?
Remember the relation:
distance = rate*time.
We know that the distance is 3 miles (done twice).
First, the rate is 2x and then the rate is x, then the time it took the first half is:
t = 3mi/2x
And for the coming back:
t = 3mi/x
Then the total time for the trip is:
T = 3mi/2x + 3mi/x = 3mi( 1/2x + 1/x) = 3mi*( 3/2x).
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which expression represent the quotient of seven and four
The expression that represents the quotient of seven and four is 7/4
How to determine the expression?The statement is given as:
quotient of seven and four is 7/4
Quotient means divide
So, the interpretation of the expression is seven divide four i.e. 7/4
Hence, the expression that represents the quotient of seven and four is 7/4
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[Worth 30 Points] NEED HELP!!!
To estimate the height of a mountain, two students find the angle of elevation from a point (at ground level) b=740meters from the base of the mountain to the top of the mountain is β=60∘. The students then walk a=1850 meters straight back and measure the angle of elevation to now be α=37∘. If we assume that the ground is level, use this information to estimate the height of the mountain.
The height of the mountain is: ______ Meters.
Explain how your answer measure below. Be sure to show all of your work.
The height of the mountain estimated by two students is 2,467.98 meters.
Height of the mountain
The height of the mountain is calculated as follows;
tanα = h/( a + b + x)
where;
x is the distance between end of b and htan37 = h/(1850 + 740 + x)
tan37 = h/(2590 + x)
h = tan37(2590 + x)
h =1,951.82 + 0.7536x ---- (1)
tanβ = h/(b + x)
tan60 = h/(740 + x)
h = tan60(740 + x)
h = 1,281.68 + 1.732x ---- (2)
Solve (1) and (2) together
1,951.82 + 0.7536x = 1,281.68 + 1.732x
1,951.82 - 1,281.68 = 1.732x - 0.7536x
670.14 = 0.9784x
x = 684.93 m
h = 1,281.68 + 1.732x
h = 1,281.68 + 1.732(684.93)
h = 2,467.98 m
Thus, the height of the mountain estimated by two students is 2,467.98 meters.
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