Answer:
I think it is 336 ways the medals can be given out.
Step-by-step explanation:
Solve.
3x+2y−z=8
2x+2z=−4
x+3y=4
Enter your answer, in the form (x,y,z), in the boxes in simplest terms.
The solution of the system of linear equations is (x, y, z) = (1, 1, - 3).
How to resolve a system of linear equations
In this problem we find a system of three linear equations with three variables, which can be resolved by several methods. In this case, we shall use the method of substitution. First, clear the variable x in the third equation:
x = 4 - 3 · y
Second, substitute x in the first two equations:
3 · (4 - 3 · y) + 2 · y - z = 8
12 - 9 · y + 2 · y - z = 8
- 7 · y - z = - 4
2 · (4 - 3 · y) + 2 · z = - 4
8 - 6 · y + 2 · z = - 4
- 6 · y + 2 · z = - 12
Third, clear z in the first equation derived in the previous step:
z = 4 - 7 · y
Fourth, substitute z in the second equation derived in the second step:
- 6 · y + 2 · (4 - 7 · y) = - 12
- 6 · y + 8 - 14 · y = - 12
- 20 · y = - 20
y = 1
Fifth, calculate y and x:
z = 4 - 7 · 1
z = - 3
x = 4 - 3 · 1
x = 1
The solution of the system of linear equations is (x, y, z) = (1, 1, - 3).
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Cosx-1=0[tex]Cos(x)-1=0[/tex]
The solution of the given trigonometric form equation as required in the complete task content is; x = nπ where n is any real number integer value.
What is the solution of the given trigonometric equation as in the task content?It follows from the task content that the solution to the given trigonometric equation is to be determined.
Given;
Cos(x) - 1 = 0
Add 1 to both sides of the equation;
Cos (x) = 1
Therefore, the value of x can be determined by evaluating the cos inverse of (-1).
Hence,
x = Cos-¹(1)
x = nπ (where n is any integer real number value).
Ultimately, the solution of the given trigonometric form equation as required in the complete task content is; x = nπ where n is any real number integer value.
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Taylor is curious to know how different types of music will impact how long it takes someone to finish their homework. She gathers a group of 12 year olds and breaks them into groups of 3. The first group listens to nothing. The 2nd group listens to classical, the 3rd listens to pop music, and the 4th listens to heavy metal. Each group needs to read 20 pages of the same book and answer the same set of 20 math questions. She times each group and compares.
a) Find the Independent Variable
b) Find the dependent variable
c) Find the Control Group
d) Find the experimental group
e) Find 3 constants
A dog is 9 times as heavy as a cat, a hamster is 20 times as light as a cat, and a mouse is 6 times as heavy as the hamster. How many times is the dog as heavy as a mouse?
Answer:
30
Step-by-step explanation:
Let the cat have a weight of x.
Then, the dog weighs 9x.
The hamster weighs x/20.
The mouse weighs 3x/10.
So, the dog is 9/(3/10) = 30 times as heavy.
The weight of the dog is 30 times the weight of the mouse.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Let the weight of the dog be x,
A dog is 9 times as heavy as a cat,
weight of the dog = 9x - - - - -(1)
A hamster is 20 times as light as a cat
Weight of the hamster = x /20
A mouse is 6 times as heavy as a hamster.
Weight of the mouse = 6(x /20)
m(20/6) = x
Now, put x = m(20/6) in equaiton 1,
weight of the dog = 9[m(20/6)]
weight of the dog = 30m
Thus, the weight of the dog is 30 times the weight of the mouse.
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Michael Wittry has been investing in his Roth IRA retirement account for 21 years. Two years ago, his account was worth $215,613. After losing 13 of its original value, it then gained 12 of its new value back. What is the current value of his Roth IRA
If two years ago, his account was worth $215,613. After losing 13 of its original value, it then gained 12 of its new value back. The current value of his Roth IRA is: $215,613.
Current valueFirst step is to calculate the value loss
Value loss=1/3× original value
Value loss= 1/3× $215,613
Value loss= $71,871
Second step is to calculate the new value
New value=$215,613-$71,871
New value= $143,742
Third step is to calculate the value gained
Value gained= 1/2× new value
Valued gained=1/2× $143,742
Valued gained=$71,871
Fourth step is to calculate the current value
Current value= $143,742+$71,871
Current value=$$215,613
Therefore If two years ago, his account was worth $215,613. After losing 13 of its original value, it then gained 12 of its new value back. The current value of his Roth IRA is: $215,613.
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Question 6 of 10
A triangle has two sides of lengths 4 and 7. What value could the length of
the third side be? Check all that apply.
DA7
B. 17
C. 9
D. 3
E 11
F. 5
all that sides which can be applicable in the given side of triangle are:
F.5
A.7
C.9
WHICH THEOREM IS APPLICABLE FOR FINDING THE THIRD SIDE OF TRIANGLE ?Third Side of a Right Angle Triangle Pythagorean Theorem. The length of the hypotenuse in a right triangle can be determined using the Pythagorean Theorem. You can determine the length of the missing side using algebra and square roots as long as you are only given two lengths.
CALCULATIONa,b and c are the sides of a triangle if it satisfies:
a<b+c , b<a+c and c<b+a
Here, a=4 and b=7
We have to find c
i.e. all those c which satisfies:
4<7+c , 7<4+c and c<4+7=11
D.3 it is not true since it doesn't satisfies second inequality
F.5 it is true
A.7 it is true
C.9 it is true
E.11 This is clearly false, since it doesn't satisfies inequality third
F.5 This is clearly false, since it doesn't satisfies inequality third
Hence, correct options are:
F.5
A.7
C.9
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how many unique straight lines in parallelogram
Answer:
4 lines
Step-by-step explanation:
We know that a parallelogram is constructed using two parallel lines intersecting other pairs of parallel lines so basically we require 4 lines to construct a parallelogram.
Answer:4
Step-by-step explanation:
Suppose we want to choose 6 objects, without replacement, from 12 distinct objects. (a) If the order of the choices matters, how many ways can this be done? (b) If the order of the choices does not matter, how many ways can this be done?
(a) There are 665280 ways of selection if the order of the choices matters.
(b) There are 924 ways of selection if the order of the choices does not matters.
(a) If the order of the choices matters, then we must use the permutation formula that is
[tex]^nP_r = \frac{n!}{(n - r)!}[/tex]
Here n is the total no. of objects and r is chosen objects
We have n = 12
r = 6
After we substitute the value we get
[tex]^{12}P_6 = \frac{12!}{(12 - 6)!}[/tex]
[tex]^{12}P_6 = \frac{12!}{6!}[/tex]
[tex]^{12}P_6[/tex] = 665280
Thus, there are 665280 ways of selection if the order of the choices matters
(b) If the order of the choices does not matter, then we must use the combination formula that is
[tex]^nC_r = \frac{n!}{r!(n - r)!}[/tex]
After we substitute the value we get
[tex]^{12}C_6 = \frac{12!}{6!(12 - 6)!}[/tex]
[tex]^{12}C_6 = \frac{12!}{6! 6!}[/tex]
[tex]^{12}C_6 =[/tex] 12×11×10×9×8×7×6! / 6!×6!
[tex]^{12}C_6 =[/tex] 12×11×10×9×8×7/ 6!
[tex]^{12}C_6 =[/tex] 665280/ 720
[tex]^{12}C_6 =[/tex] 924
Thus, there are 924 ways of selection if the order of the choices does not matters.
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219 +485 = 348 + please
Answer: please=356
Step-by-step explanation:
219 +485 = 348 + please
704=348 + please
please=356
When the number of miles driven equals 0, why is the cost per month not equal to 0? Why does the graph have a positive slope?
Answer:
I think it's because of the down payment and the positive slope because you are going to pay in installments by months.
A and B are vertical angles.
If m/A = (2x +29)° and m B (3x - 17)°, then find the measure of B.
=
The required measure of the angle m∠B is 121°.
Given that,
Angle A and B are two vertical equal angles.
m∠B = 3x - 17
m∠A = 2x + 29
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
m∠A = m∠B
2x + 29 = 3x - 17
-x = - 46
x = 46
Now,
m∠B = 3 *46 - 17
m∠B = 138 - 17
m∠B = 121°
Thus, the required measure of the angle m∠B is 121°.
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given z (x)=15x-x^2+3
Answer:
○ [tex]z(x - 1) = -x^2 + 17x - 13[/tex]
Step-by-step explanation:
We are told that:
[tex]z(x)= 15x - x^2 + 3[/tex],
and told to find an expression for [tex]z(x - 1)[/tex].
In order to find [tex]z(x - 1)[/tex], we have to replace [tex]x[/tex] in the definition of [tex]z(x)[/tex] with [tex](x-1)[/tex]:
[tex]z(x - 1) = 15(x -1) - (x - 1)^2 + 3[/tex]
Now we can simplify:
⇒ [tex]z(x-1) = 15x - 15 - (x - 1)^2 + 3[/tex] [Distributing 15 into the first brakets]
⇒ [tex]z(x-1) = 15x - 15 - (x^2 - 2x + 1) + 3[/tex]
⇒ [tex]z(x-1) = 15x - 15 - x^2 + 2x - 1 + 3[/tex] [Distributing the minus sign]
⇒ [tex]z(x - 1) = 17x - x^2 -13[/tex] [Combining like terms]
⇒ [tex]z(x - 1) = -x^2 + 17x - 13[/tex]
Therefore, the first option is the correct one.
Gabby worked 30 hours in 4 days. Determine the rate for ratio of the two different quantities.
30/34 hours per day
4/30 hours per day
30/4 hours per day
4/34 hours per day
The required rate for ratio of the two different quantities i.e
Gabby worked 30/4 hours per day.
Option (c) is correct.
What is arithmetic?Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.
Given:
Gabby worked 30 hours in 4 days.
According to given question we have
The ratio of the two quantities of the different kind and in the different units is a fraction that shows how many times one quantity is of the other.
By the use of arithmetic we have,
Gabby worked 30 hours in 4 days means
4 days= 30 hours
1 days = 30/4 hours
Therefore, the required rate for ratio of the two different quantities i.e
Gabby worked 30/4 hours per day.
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Answer: 30/4 hours per day
Step-by-step explanation:
Assistant Manager Clyde works as a part-time assistant manager for the Barkley Coffeehouse to earn money to help pay for his college expenses. He makes $11.50 per hour. The coffeehouse sells whole bean coffee, mugs, and other coffee products. Clyde earns $0.50 for each of these items he sells. Last week he worked 30 hours and earned $364. How many coffee products did he sell last week?
The number of coffee product he sells is 38.
How to find the number of coffee products he sells?He makes $11.50 per hour.
He earns $0.50 for each of these items he sells.
Last week he worked 30 hours and earned $364.
Therefore, the number of coffee product he sells last week can be calculated as follows:
let
x = number of coffee product he sells.
364 = 11.50(30) + 0.50(x)
364 = 345 + 0.50x
364 - 345 = 0.50x
19 = 0.5x
divide both sides by 0.5
x = 19 / 0.5
x = 38
Therefore, the number of coffee product he sells is 38.
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PLEASE HELP! Triangle BCD has the following side lengths: BC = 60, CD = 50
Triangle RST has the following side lengths: RS = 11x-4, ST = 70
What is the value of x? (put just the number in the first box)
What is the length of side RS? (put just the number in the second box)
The value of x is 11 units and the length of side RS = 11x-4 is 117 units.
with measurement BC = 60, CD = 50.
Triangle RST : RS = 11x-4, ST = 70
What is similarity?Two figures are said to be similar if they are the same shape. In more mathematical language, two figures are similar if their corresponding angles are congruent , and the ratios of the lengths of their corresponding sides are equal.
Given:
BC = 60 and CD = 50
RS = 11x - 4 and ST = 70
Now, considering
BC : CD = RS : ST
60 : 50 = 11x - 4 : 70
60/50 = (11x - 4)/70
50 * (11x - 4) = 70 * 60
11x - 4 = 84
11x = 88
x = 11
So, RS = 11x - 4
RS = 11 x 11 - 4
RS = 117
Hence, the value of x is 11 and the length of side RS is 117
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Multiple choice: Which of the following steps below would be a good first step when solving the equation 2x+5=11
Divide both sides by 2
Add 5 to both sides of the equation
Subtract 5 from both sides of the equation
Add 11 to both sides of the equation
Answer:
easy
Step-by-step explanation:
How to solve a system of equations by elimination.
Write both equations in standard form.
Make the coefficients of one variable opposites.
Add the equations resulting from Step 2 to eliminate one variable.
Solve for the remaining variable.
Substitute the solution from Step 4 into one of the original equations.
E= 1R solve for R pls help me I don’t understand
Answer:
r = e or 2.718282
Step-by-step explanation:
a) simplify both sides of the equation
2.718282 = r
b) flip the equation
r = 2.718282
Please help me
Thank you
Answer: 3 gallons per hour
Step-by-step explanation: 14-(3x) =5 14-5=9 9/3=3
Shinya went to the salon. The cost if her haircut was $18.00. He tipped the barber 20%. What was the total cost
?
What are the coordinates of point A?
Answer:
It's coordinates are (1,-2)
QUESTION 5
(a) Differentiate the following
(i)
y=e²x - 3e-4x
Answer: e² - 4
Step-by-step explanation:
Differentiate of e²x - 3e-4x is e² - 4
Answer:
[tex]\dfrac{\text{d}y}{\text{d}x} = 2e^{2x}+12e^{-4x}[/tex]
Step-by-step explanation:
Given function:
[tex]y=e^{2x}-3e^{-4x}[/tex]
[tex]\boxed{\begin{minipage}{3.7cm}\underline{Differentiating $ax$}\\\\If $y=ax$, then $\dfrac{\text{d}y}{\text{d}x}=a$\\\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Differentiating $e^{f(x)}$}\\\\If $y=e^{f(x)}$, then $\dfrac{\text{d}y}{\text{d}x}=f\:'(x)e^{f(x)}$\\\end{minipage}}[/tex]
Therefore:
[tex]\begin{aligned}\implies \dfrac{\text{d}y}{\text{d}x} & = \dfrac{\text{d}}{\text{d}x} e^{2x}-\dfrac{\text{d}}{\text{d}x}3e^{-4x}\\\\& =2 \cdot e^{2x}-(-4)\cdot 3 e^{-4x} \\\\ &= 2e^{2x}+12e^{-4x}\end{aligned}[/tex]
Jessica earns $10.35/hour at her part-time job. Usually she works 24 hours a week. If she can only put aside 30% of her earnings, about how many weeks will she need to work in
order to save money for a new cell phone at $399?
Select one:
A. 3
B. 6
C. 5
D. 4
Answer:
B. 6
Step-by-step explanation:
$10.35 × 24 = 248.4 per week
248.4 × 30% = 74.52 {30% of her earnings}
$74.52 × 6 weeks = $447.12
∴ She needs to work for 6 weeks in order to save up to $399
Can someone please explain this to me? Thank youuu:)
Answer:
B: 3x+(4x+2)=180
Step-by-step explanation:
Supplementary angles are those angles that sum up to 180 degrees. The question gives you the two angles that compose the 180 degree angle thus you get the equation:
Angle 1 + Angle 2 = Supplementary Angle
In this case we see that these two angles are Angles B and C and a supplementary angle is 180 degrees thus:
(4x+2)+3x = 180
Furthermore this also allows you to find x.
All flowers need water
Some trees need water
Some flowers are trees
Valud or Invalid
valid . some trees grow flowers i belive
3)
Chicken cost $7.19 per pound. You buy 0.82 pounds at the supermarket.
How much did you spend?
Answer:
$5.90
Step-by-step explanation:
(7.19)(.82) Put these numbers in your calculator and multiply them together.
5.8958 Round to the nearest cent
$5.90
Prepare for Rigid Transformations Think about what you know about geometric figures and parallel lines. Fill in each box. Use words, numbers, and pictures. Show as many ideas as you can.
Step-by-step explanation:
Parallel Lines are lines that do not intercept with eachother. They have the same slope yet have different y-intercepts.
Draw two lines not touching.
Example
[tex]y = 5x + 1[/tex]
[tex]y = 5x + 2[/tex]
No examples
[tex]y = 5x + 2[/tex]
[tex]y = - \frac{1}{5} x + 2[/tex]
Hope this helps!
The terminal side of an angle theta in standard position passes through the point -6(-4,). Use the figure to find the following value. r
Answer is - 2 [tex]\sqrt{3}[/tex] / 13
Cosecant Given a point P(x, y) on the terminal side of an angle θ in standard position
cosθ = cos (π + d) (d is the inner angle of the tringle)
= - cos 2
= - 4 / - [tex]\sqrt{(- 6^{2} + (- 4^{2} )[/tex]
= - 4 / - [tex]\sqrt{36 + 16 }[/tex]
= - 4 / -[tex]\sqrt{52}[/tex]
= - 4 / 2[tex]\sqrt{13}[/tex]
= - 2 / [tex]\sqrt{13}[/tex]
multiply by [tex]\sqrt{13}[/tex]
we get,
= - [tex]\frac{2 \sqrt{13} }{13}[/tex]
Formulae :
Arc cosecant y = arcs(x) = csc-1(x). Another way to write x = csc(y).
Arccosine y = arcos(x) = cos-1(x). Another way to write x = cos(y).
Arc cotangent y = arcos(x) = cot-1(x). Another way to write x = cot(y).
Arc secant y = arcsec(x) = sec-1(x). Another way to write x = sec(y).
Arcsine y = arcsine(x) = sin-1(x). Another way to write x = sin(y).
Arctangent y = arctan(x) = tan-1(x). Another way to write x = tan(y).
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Solve the inequality and express your answer in interval notation. x^2-12x+3<0
Solution:
B.) [tex](6-\sqrt{33}, 6+\sqrt{33})[/tex]
Hope this helps! If so, please lmk! Thanks and good luck!
A city has a population of 210,000 people. Suppose that each year the population grows by 4.5% . What will the population be after 5 years?
The population of a city after 5 years would be 261698.
We know the the formula for the exponential growth of the population is,
P(t) = a(1+r)^t
where, a is the initial population
t is the time period
r is the rate of growth
In this question, we have a = 210000, %R = 4.5
So, r = 0.045
We need to find the population after 5 years.
t = 5
Using above formula,
P = 210000 × ( 1 + 0.045)^5
P = 210,000 × (1.045)^5
P = 210,000 × 1.25
P = 261698.2
P ≈ 261698
Therefore, the population of a city after 5 years would be 261698.
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Two boy scouts were selling popcorn for a fundraiser at a local grocery store and made $640. They sold twice the amount of kettle corn as butter popcorn, and 6 more bags of cheddar popcorn than kettle corn. If kettle corn cost $15 a bag, butter popcorn cost $8 per bag, and cheddar popcorn cost $10 per bag, how much of each type of popcorn did they sell? Write an equation to solve the problem.
They sold 10 bags of butter popcorn, 20 bags of kettle corn and 26 bags of cheddar cheese.
Here, we are given that two boy scouts were selling popcorn for a fundraiser.
Their total revenue = $640
Let the bags of butter popcorn be x
then, the bags of kettle corn sold = 2x
and the bags of cheddar popcorn sold = 2x + 6
Cost of kettle corn = $15/ bag
Cost of butter popcorn = $8/ bag
Cost of cheddar popcorn = $10/ bag
Thus, the total revenue from from kettle corn = $30x
total revenue from from butter popcorn = $8x
total revenue from from cheddar popcorn = $10(2x + 6)x
Thus, we will get the following equation-
30x + 8x + 10(2x + 6) = 640
38x + 20x + 60 = 640
58x + 60 = 640
58x = 580
x = 580/ 58
x = 10
Thus, 2x = 20 and 2x + 6 = 26
Hence, they sold 10 bags of butter popcorn, 20 bags of kettle corn and 26 bags of cheddar cheese.
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