The equation to represent the situation is like so:
[tex]x+(x-12)+3(x-12)=332[/tex]
Simplify.
[tex]x+x-12+3x-36=332[/tex]
[tex]5x-48=332[/tex]
[tex]5x-380=0[/tex]
Solve for the variable x.
[tex]5x=380[/tex]
[tex]x=76[/tex]
[tex]first\ man =x\\second\ man =x-12\\machine=3(x-12)[/tex]
[tex]first\ man=76\\second\ man=64\\machine=192[/tex]
Verify.
[tex]x+(x-12)+3(x-12)=332[/tex]
[tex]76+(76-12)+3(76-12)=332[/tex]
[tex]76+64+192=332[/tex]
[tex]332=332[/tex]
[tex]LS=RS[/tex]
Suppose that you are a member of the typical American household and your family carries a credit card debt of
$7942. Use the TVM (Time-Value-of-Money) Solver to model a few credit card scenarios. (Note: Use months
rounded to the nearest hundredths on all calculations.)
1. If the average annual interest rate is 17.11%, how many months will it take the average American family
to pay off their debt of $7,942 if they make a minimum payment of $175 each month and no additional
purchases are made?
2. How much interest did you pay during this time?
1. At an annual interest rate of 17.11%, an average family needs 74 months to settle $7,942 at a $175 monthly payment.
2. The total interest is $4,932.10.
What is a monthly payment?The monthly payment is the amount paid each month to settle the loan within its maturity period.
The monthly payment can be computed using an online finance calculator.
We can also determine the period of payment using the same online finance calculator as below.
Data and Calculations:I/Y (Interest per year) = 17.11%
PV (Present Value) = $7,942
PMT (Periodic Payment) = $-175
FV (Future Value) = $0
Results:
N = 73.566
Sum of all periodic payments = $12,874.10
Total Interest = $4,932.10
Thus, while it will take 74 months for the average American family to pay off the loan of $7,942 with a monthly payment of $175 at 17.11% interest, the total interest paid is $4,932.10.
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The red square is the image of the blue square after a SINGLE transformation. Use two or more complete sentences to describe each of the FOUR different transformations that could produce the image.
The transformations which can lead to the red square image of the blue Square are; Translation, Reflection, Rotation.
What transformations lead to the image?Translation is when we slide a figure in any direction. The translation of the shape can be by moving the blue leftward or rightward and the then downward.Reflection is when we flip a figure over a line. The reflection involves reflect the blue Square over the line; y = x.Rotation is when we rotate a figure a certain degree around a point. The rotation is by rotating the blue Square over 180⁰.Read more on transformations;
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Law of Cosines
HELP!!!!!
Answer:
[tex]\displaystyle 21 \approx c[/tex]
Explanation:
Solving for Angles
[tex]\displaystyle \frac{a^2 + b^2 - c^2}{2ab} = cos\angle{C} \\ \frac{a^2 - b^2 + c^2}{2ac} = cos\angle{B} \\ \frac{-a^2 + b^2 + c^2}{2bc} = cos\angle{A}[/tex]
Do not forget to use [tex]\displaystyle arccos[/tex] or [tex]\displaystyle cos^{-1}[/tex]towards the end, or the result will be thrown off.
Solving for Edges
[tex]\displaystyle b^2 + a^2 - 2ba\:cos\angle{C} = c^2 \\ c^2 + a^2 - 2ca\:cos\angle{B} = b^2 \\ c^2 + b^2 - 2cb\:cos\angle{A} = a^2[/tex]
Take the square root of the result in the end, or you will throw yourself off.
Well, let us get to work:
[tex]\displaystyle 13^2 + 29^2 - 2[13][29]cos\:41 = c^2 \\ 169 + 841 - 754cos\:41 = c^2 \\ 1010 - 754cos\:41 = c^2 \\ \\ \sqrt{440,94897651...} = \sqrt{c^2} \\ 20,99878512... = c \\ \\ \boxed{21 \approx c}[/tex]
I am joyous to assist you at any time.
PLS HELP ASAP DUE TODAY
A teacher writes the name of each of her 25 students on a slip of paper and places the papers in a box. To call on a student,
she draws a slip of paper form the box. Each paper is equally likely to be drawn, and the papers are replaced in the box
after each draw.
What is the probability of calling on the same student twice in a row?
a. 0.0016
c.
0.56
b. 0.36
d.
0.04
Please select the best answer from the choices provided
the answer would be 0.56
Answer:
a: 0.0016
Step-by-step explanation:
Got it right on the test.
Hope this helps :)
Write 19% as a fraction.
Answer:
19/100
Step-by-step explanation:
Answer:
19/100
Step-by-step explanation:
The answer is 19/100 because the percentage should be out of 100. Therefore, the fraction is 19/100.
Zachary has 10 9/16 cups of dough to make dumplings. If he uses 13/16 cup of dough for each dumpling, how many dumplings can Zachary make?
Answer:
Zachary can make 13 dumplings.
Step-by-step explanation:
We know the size of the groups (13/16 cups) and the total (10 9/16 cups of dough). We're trying to find the number of groups that would fit in our total (10 9/16 cups). To find that out, we need to compute:
13\16 x ? =10 9/16
10 9/16 divided by 13/16 = ?
10 9/16 x 16/13
Which of these is equal to sin 58°?
Answer:
C Cos32
Step-by-step explanation:
What’s the inverse of the function?
f(x)=3^x+1
[tex]y= f(x) = 3^x+1\\\\\text{Replace x with y and solve for y}\\ \\~~~~~~x=3^y+1\\\\\implies 3^y = x-1\\ \\\implies \ln(3^y) = \ln(x-1)\\\\\implies y \ln 3= \ln(x-1)\\\\\implies y= \dfrac{\ln(x-1)}{\ln 3}\\\\\implies f^{-1}(x) = \dfrac{\ln(x-1)}{\ln 3}[/tex]
Solve the equation on the
interval [0,21).
2 csc x + 17 = 15 + CSC X
Answer:
7π/6, 11π/6
Step-by-step explanation:
2cscx + 17 = 15 + cscx
1. Subtract cscx and 17 from both sides ⇒ cscx = -2
2. cscx = 1/sinx ⇒ 1/sinx = -2
3. Multiply by sinx and divide by -2 ⇒ sinx = -1/2
When is sinx equal to -1/2? ⇒ 7π/6, 11π/6
The solution of the equation 2cosec x+17 = 15+cosec x is 7π/6 and 11π/6.
What is the solution of the given equation in the interval [0, 2π)?Given:
The equation which is given is 2Cosec x + 17 = 15 + Cosec x.The interval is [0,2π).Find:
The solution of the given equation.Solution:
2Cosec x + 17 = 15 + Cosec x
⇒ 2Cosec x - Cosec x = 15 - 17
⇒ Cosec x = -2
Now, 1/sinx = -2
⇒ sinx = -1/2
we know, sin 30° = 1/2
Since, sinx is negative,
x will be in 3rd and 4th quadrant.
value in 3rd quadrant = 180° + 30° = 210°
value in 4th quadrant = 360° - 30° = 330°
So, x = 210° = 210 * π/180 = 7π/6
Also, x = 330° = 330 * π/180 = 11π/6
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O is the center of the regular octagon below. Find its area. Round to the nearest tenth
if necessary.
Based on characteristics of regular polygons, the area of the regular octagon with an apothema of 17 units is approximately 239.415 square units. #SPJ1
How to find the area of a regular polygon
A polygon is regular when all sides and central angles have the same length.The area of a regular polygon (A) can be found in terms of the number of sides (n) and the apothema (a), whose length is 17, by using the following formula:
A = 0.25 · n · a² · tan (180/n) (1)
If we know that n = 8 and a = 17, then the area of the regular octagon is:
A ≈ 239.415
Based on characteristics of regular polygons, the area of the regular octagon with an apothema of 17 units is approximately 239.415 square units. #SPJ1
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What is the area of this triangle?
Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.
in²
The figure contains a triangle. One side is 13 inches. A second side is 7.5 inches. The angle between the given sides is 94 degrees.
Answer:
Area = 48.6 in²
Explanation:
The area of the triangle can be calculated using the side-angle-side method as follows:
Area = 0.5 * first side * second side * sin(angle included between the two sides)
This rule is illustrated in the attached image.
Now, we have:
first side = 13 in
second side = 7.5 in
The angle included between the two sides = 94 degrees
The given angle is included between the two given sides, therefore, we can apply the above rule to get the area.
Area of triangle = 0.5 * 13 * 7.5 * sin(94)
Area of triangle = 48.63 which is approximately 48.6 in²
Hope this helps :)
fx) = X. What is g(x)?
f(x) = x
g(x)?
PLEASE HELP ASAP!!!!
Answer:
C
Step-by-step explanation:
vertex form:
[tex]y = {a(x - h)}^{2} + k[/tex]
the negative sign in front of x^2 is also -1, which is the "a". A controls if the parabola will opek up or down, and the width of the function. In this problem, the parabola opens down. the -3 corresponds to "k" in vertex form. K is the vertical shift or the y coordinate of the vertex. If k is positive it moves up, and if it is negative it moves down. Because of the -3, the vertex of the parabola will move down 3 units on the y-axis.
Let the vector v v have an initial point at ( 1 , − 7 ) (1,−7) and a terminal point at ( 3 , − 2 ) (3,−2). Determine the components of vector v . v.
Answer: The vector is < 2, 5 >
==========================================================
Explanation:
Label the initial point (1,-7) as point P and (3,-2) as point Q.
The x coordinate of P is 1The x coordinate of Q is 3This is a change of +2, meaning we move 2 units to the right.
Therefore, the x component of the vector is +2 or simply 2.
The y coordinate of P is -7The y coordinate of Q is -2This is a change of +5 when moving from P to Q. We have moved 5 units up. The y coordinate of the vector is +5 or simply 5.
Overall, the vector is < 2, 5 > which tells the reader "move 2 units to the right and 5 units up.
Refer to the diagram below.
Which of the following gives an example of
an exponential function?
a. y = 3x^2
b. y = x^-5
c. y = 1.5^x
D. = x^2 - x
Is 3,978×-32 positive or negative
Answer:
negative
Step-by-step explanation:
A positive times a negative is a negative
Thomas works 12 days out of every month.
1. Does Thomas work the same percent of days each month? Explain.
Answer:
no (see below)
Step-by-step explanation:
Not all of the months have the same amount of days therefore Thomas does not work the same percentage of days each month.
This figure represents a platform on a stage. The stage crew needs to paint it black. One gallon of paint will cover 40 square yards.
How many full gallons of paint does the crew need to buy in order to paint the entire platform?
Enter your answer in the box.
gallons
Answer:
it is 4 or 3 i think 4 more tho
Step-by-step explanation:
Answer:
14
Step-by-step explanation:
What is the area of the shaded sector of Point B below?
Answer:
A) 175π / 9 squared inches,
Step-by-step explanation:
Radius = 10 inches
AB = BD = 10 = radius
Triangle ABD is isosceles
Angle DAB = Angle BDA = 35 degrees,
Base angles theroem
35 + 35 + x = 180, angles in triangle
x = 180 - 70
x = 110 degrees
Angle DBC is supplementary with ABD
110 + x = 180
x = 70
70 degrees is angle for the sector
70 is 70/360, 7/36 of the circle
The area will also be 7/36 of the circle area
Area of circle = πr^2
Area = 100π
Area of sector = (100π * 7) / 36
Area of sector = 700π / 36
Simplified area = 175π / 9 squared inches
Which of the following represents a set of irrational numbers?
A: {√3, √16, √21, √25}
B: {3.1, 1.234..., √36, π}
C: {12π/4, √2/4, 1.121214…, √5 }
D {23.1, 1.234, √36, 4π }
Answer:
C
Step-by-step explanation:
[tex]\text{All other options contain rational numbers, such as} ~\sqrt{36} , \sqrt{25}, \sqrt{16}[/tex]
If it takes 3.6 minutes to fill a 3000ml container, how long will it take to fill a 1.5L container?
Answer:
1.8 min
Step-by-step explanation:
This question is easier to answer than it would be in general.
3000 mL = 3 L
1.5L is exactly half of that, so the time to fill the 1.5L container is half the time it takes to fill the 3L container.
Half of 3.6 minutes is 1.8 minutes
3/5 of the students in Süd- class are in chorus. If there are 25 people in her class, how many are in the chorus?
What is the area of a circle with a diameter of 32?
Answer:
How much is 32 cm in diameter?
Centimeters to Inches table
centimeters inches
32cm 12.60
33cm 12.99
34cm 13.39
35cm 13.78
Step-by-step explanation:
Answer:
A
≈
804.25
I am sure just trust me ;)
Handsome Jack is buying a pony made of Diamonds
Answer:
so what should we do?!?!?!?!¡!?!
Polly is a server at a
restaurant. A table spends $34
and leaves Polly an 18% tip.
What is Polly's tip?
Answer:
They gave her a $6.12 tip
Step-by-step explanation:
You have to multiply the total ($34) by the Percent (18% = 0.18), and then you will have your final answer.
giving brainliest :D
show steps in a simple way (not to long of an example ty :))
Answer:
[tex]\boxed{8x+6 \: units= base}[/tex]
Step-by-step explanation:
Altitude = 3x
Area = 12x² + 9x
We know that
Area of right triangle = ½ × base × altitude
Then,
12x² + 9x = ½ × 3x × base
[tex]12x ^ { 2 } +9x= \frac{ 3x }{ 2 } \times \: base[/tex]
[tex]\frac{6x\left(4x+3\right)}{3x} = \frac{3x\times \: base}{3x}[/tex]
[tex]\frac{6x\left(4x+3\right)}{3x} = base[/tex]
[tex]\underline{\underline{8x+6 \: units= base}}[/tex]
________
Hope it helps ⚜
How do you find total pension expense?
Answer:
Total periodic pension costs (TPPC) is equal to the contributions plus change in the pension liability during the year. Each period, the periodic pension cost is recognized in profit or loss (P&L) and/or in other comprehensive income (OCI).
A researcher is studying the growth of bacteria. He starts eith 280 of the bacteria. It grows continuously at a rate of 6% per hour. How many bacteria will there be in 16 hours?
Classify each number as rational or irrational. 3.31662479...
Answer:
3.31662479... is irrational
Step-by-step explanation:
The number 3.31662479... is written in a decimal form:
It is a nonterminating decimal (look at the three dots at the end)
and a nonrepeating decimal (no repeating pattern)
So it is irrational.
Answer:
IrrationalStep-by-step explanation:
The given number is :
3.31662479...The three dots at the end of the number indicates that it is non-terminating
Also you see that the digits do not repeat, hence it is also non-repeating
Definition of An Irrational Number
⇒ The decimal expansion of an irrational number is neither terminating nor recurring.
As it satisfies the criteria, the given number is irrational
help an someone help