Answer:
5900 at 11%
3600 at 8%
Step-by-step explanation:
x= invested at 11%
y= invested at 8%
x+y=9500
.11x+.08y=937
Mulitply the first equation by .11
.11x+.11y= 1045
Subtract this and the second equation
(.11x+.11y)-(.11x+.08y)=1045-937
.03y=108
y=3600
SOlve for x
x+3600=9500
x=5900
4. Write the number 3.8 in the form using integers, to show that it is a rational number. 8 11 38 10 10 38 100
Answer:
38 divided by 10 equals 3.8
find the differential equation of this function and indicate the order y = e^3x (acos3x +bsin3x)
Answer:
y"-6y'+18y=0
Second order
Step-by-step explanation:
Since there are 2 constants, the order of the differential equation will be 2. This means we will need to differentiate twice.
y = e^(3x) (acos3x +bsin3x)
y'=3e^(3x) (acos3x+bsin3x)
+e^(3x) (-3asin3x+3bcos3x)
Simplifying a bit by reordering and regrouping:
y'=e^(3x) cos3x (3a+3b)+e^(3x) sin3x (3b-3a)
y"=
3e^(3x) cos3x (3a+3b)+-3e^(3x) sin(3x) (3a+3b)
+3e^(3x) sin3x (3b-3a)+3e^(3x) cos(3x) (3b-3a)
Simplifying a bit by reordering and regrouping:
y"=
e^(3x) cos3x (9a+9b+9b-9a)
+e^(3x) sin3x (-9a-9b+9b-9a)
Combining like terms:
y"=
e^(3x) cos3x (18b)
+e^(3x) sin3x (-18a)
Let's reorder y like we did y' and y".
y = e^(3x) (acos3x +bsin3x)
y=e^(3x) cos3x (a) + e^(3x) sin3x (b)
Objective is to find a way to combine or combine constant multiples of y, y', and y" so that a and b are not appearing.
Let's start with the highest order derivative and work down
y"=
e^(3x) cos3x (18b)
+e^(3x) sin3x (-18a)
We need to get rid of the 18b and 18a.
This is what we had for y':
y'=e^(3x) cos3x (3a+3b)+e^(3x) sin3x (3b-3a)
Multiplying this by -6 would get rid of the 18b and 18a in y" if we add them.
So we have y"-6y'=
e^(3x) cos3x (-18a)+e^(3x) sin3x (-18b)
Now multiplying
y=e^(3x) cos3x (a) + e^(3x) sin3x (b)
by 18 and then adding that result to the y"-6y' will eliminate the -18a and -18b
y"-6y'+18y=0
Also the characteristic equation is:
r^2-6r+18=0
This can be solved with completing square or quadratic formula.
I will do completing the square:
r^2-6r+18=0
Subtract 9 on both sides:
r^2-6r+9=-9
Factor left side:
(r-3)^2=-9
Take square root of both sides:
r-3=-3i or r-3=3i
Add 3 on both sides for each:
r=3-3i or r=3+3i
This confirms our solution.
Another way to think about the problem:
Any differential equation whose solution winds up in the form y=e^(px) (acos(qx)+bsin(qx)) will be second order and you can go to trying to figure out the quadratic to solve that leads to solution r=p +/- qi
Note: +/- means plus or minus
So we would be looking for a quadratic equation whose solution was r=3 ×/- 3i
Subtracting 3 on both sides gives:
r-3= +/- 3i
Squaring both sides gives:
(r-3)^2=-9
Applying the exponent on the binomial gives:
r^2-6r+9=-9
Adding 9 on both sides gives:
r^2-6r+18=0
What's the equivalent expression.
(2-7. 5)² =?
Answer:
The Answer of the above question is 30.25
Step-by-step explanation:
Hope it helps you.
What is the percent discount if a 12,500 car is now on special for 10,250?
Answer:
Step-by-step explanation:
the answer is 2250 percent is = 22.5
Answer:
18% discount
Step-by-step explanation:
Percent discount is found by the following formula:
[tex]\frac{original-discount}{original}[/tex]
In this scenario, the original is 12500 and the discount, or special is 10250.
We can plug this into the formula to get
[tex]\frac{12500-10250}{12500}[/tex]
We can simplify the numerator by subtracting, and we get that answer as 2250.
We get the remainder of the answer as 2250 divided by 12500. We divide that, and get the answer as 0.18, which can be rewritten as 18%.
Match each equation to its graph.
1. y= x-2
2. y= -2x
3. x= -2
4. y= -2
The equation of the graph is : x = -2
What is a graph?A graph is a pictorial representation of the locus of a certain point.
How to draw a graph?A graph can be drawn by picking some fixed points from the locus of the point.
Here, the straight line passes through the points are : (-2,1); (-2,2); (-2,-5);(-2,-5).
Hence, the straight line is to be parallel to the x-axis and the equation of the graph is x= -2.
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Rewrite the following expanded notation in standard form. 600,000 + 80,000 + 1,000 + 400 + 70 + 5
Answer:
this is the answer
681,474
Hi can someone answer this question please thank you
Answer:
25
Step-by-step explanation:
5:20
We want to get the second number to 100
100/20 = 5
Multiply each term by 5
5*5 : 20*5
25 : 100
x is 25
Given that,
→ 5 : 20 :: x : 100
Then we have to,
find the second number to 100.
→ 100/20
→ 5
Now multiply each term by 5 in 5:20,
→ 5 × 5 : 20 × 5
→ 25 : 100
→ x = 25
Now these ratio will be,
→ 5 : 20 :: 25 : 100
Hence, the value of x is 25.
the vertex of this parabola is at (2,-4). when the y-value us -3, the x-value is -3. what is the coefficient of the squared term in the parabolas equation?
Answer:
The coefficient of the squared term is 1/25.
Step-by-step explanation:
We are given that the vertex of a parabola is at (2, -4). We also know that y = -3 when x = -3.
And we want to determine the coefficient of the squared term of the equation.
Since we are given the vertex, we can use the vertex form of the quadratic:
[tex]\displaystyle y = a(x-h)^2+k[/tex]
Where (h, k) is the vertex and a is the leading coefficient. The leading coefficient is also the coefficient of the squared term, so we simply need to find the value of a.
Since the vertex is at (2, -4), h = 2 and k = -4. Substitute:
[tex]\displaystyle y = a(x-2)^2-4[/tex]
y = -3 when x = -3. Solve for a:
[tex]\displaystyle (-3) = a((-3)-2)^2-4[/tex]
Simplify:
[tex]\displaystyle 1 = a(-5)^2\Rightarrow a = \frac{1}{25}[/tex]
Therefore, our function in vertex form is:
[tex]\displaystyle f(x) = \frac{1}{25}\left(x-2)^2-4[/tex]
Hence, the coefficient of the squared term is 1/25.
Answer:
-5
Step-by-step explanation:
from a p e x
for every 5 people who bought $9.75 tickets to the football game, 3 people bought $14.50 tickets. If each of 35 people bought a $9.75 ticket, how many people bought the more expensive ticket?
9514 1404 393
Answer:
21
Step-by-step explanation:
The number who bought expensive tickets is 3/5 of the number who bought cheap tickets.
(3/5)(35) = 21
21 people bought the more expensive ticket.
Answer:
21 people
Step-by-step explanation:
$9.75 $14.50
5 people to 3 people
35 people to ? people
consider the proportions: 5/3 = 35/?
we need the equivalent fraction of 5/3 that has 35 on the denominator
so 5/3 = (5/3)(7/7) because 7/7 =1, and 5*3 =35
5/3 = 5*7/3*7 = 35/21
3.3.C-1
If one tablet of calcium pantothenate contains 0.5 gram, how much is contained in
n 2 1/4 tablets? How many tablets are needed to make up 2.3 grams?
A fraction calcium pantothenate contains 0.5 gram of a tablet 5 tablets to make up 2.3 grams.
To calculate the amount of calcium pantothenate contained in a given number of tablets, use the given information that one tablet contains 0.5 grams.
Amount in n 2 1/4 tablets:
To calculate the amount of calcium pantothenate in n 2 1/4 tablets, we need to calculate the total amount for each part (whole tablets and the fraction of a tablet) and then sum them up.
Amount in n whole tablets: n tablets × 0.5 grams/tablet
Amount in 1/4 tablet: (1/4)× 0.5 grams
So, the total amount in n 2 1/4 tablets would be:
Total amount = n ×0.5 + (1/4) ×0.5 grams
Tablets needed to make up 2.3 grams:
To calculate the number of tablets needed to make up 2.3 grams of calcium pantothenate, set up a proportion using the given tablet amount (0.5 grams/tablet).
Let x be the number of tablets needed.
0.5 grams/tablet = 2.3 grams / x tablets
Cross-multiply:
0.5 × x = 2.3
x = 2.3 / 0.5
x = 4.6
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the cost of 2 pairs of trousers and 3 shirts is $825 it shirt cost $50 less than the trouser. find the cost of each shirt and trouser
Answer:
a pair of trousers cost = x = 195 $
one shirt costs = x - 50 = 145 $
Step-by-step explanation:
let the cost of trouser be x.cost of shirt = (x - 50)2 pairs of trousers cost = 2x 3 shirts cost = 3(x - 50)= 3x- 150
2 trousers and 3 shirts cost = 825
=> 2x + 3x - 150 = 825
=> 5x = 975
x = 195
a pair of trousers cost = x = 195 $
a pair of trousers cost = x = 195 $ one shirt costs = x - 50 = 145 $
√12 + √10 − √2) is
(a) A positive rational number
(b) Equal to zero
(c) An irrational number
(d) A negative integer
Hello!
[tex] \bf \sqrt{12} + \sqrt{10} - \sqrt{2} = [/tex]
[tex] \bf \sqrt{ {2}^{2} \times 3} + \sqrt{10} - \sqrt{2} = [/tex]
[tex] \bf \sqrt{ {2}^{2} } \sqrt{ 3} + \sqrt{10} - \sqrt{2} = [/tex]
[tex] \bf \boxed{ 2 \sqrt{3} + \sqrt{10} - \sqrt{2}} [/tex]
Answer: (c) An irrational number
Good luck! :)
Karl wants to raise money for charity. He designs a game for people to play.
Karl uses a ten sided dice for the game. The dice is numbered 1 to 10.
Each person will roll the dice once. A person wins the game if the dice lands on a multiple of 4.
Ali plays the game once,
a) Work out the probability that Ali will win the game.
(2 m
Answer:
0.2 = 20% probability that Ali will win the game.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Total outcomes:
The 10 sides that the dice can land, which means that [tex]T = 10[/tex]
Desired outcomes:
Sides that are multiple of 4, that is, side 4 and side 8, so [tex]D = 2[/tex]
Work out the probability that Ali will win the game.
[tex]p = \frac{D}{T} = \frac{2}{10} = 0.2[/tex]
0.2 = 20% probability that Ali will win the game.
Of the delegates at a convention, 60% attended the breakfast forum, 70% attended the dinner speech and 40% attended both events. If a randomly selected delegate is known to have attended the dinner speech, the probability that he also attended the breakfast forum is
Answer:
The probability that he also attended the breakfast forum is is 0.5714 = 57.14%.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Attended the dinner speech.
Event B: Attended the breakfast forum.
70% attended the dinner speech
This means that [tex]P(A) = 0.7[/tex]
40% attended both events.
This means that [tex]P(A \cap B) = 0.4[/tex]
The probability that he also attended the breakfast forum is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.4}{0.7} = 0.5714[/tex]
The probability that he also attended the breakfast forum is is 0.5714 = 57.14%.
How far will fiona jog (in feet)
Answer:
1780 ft
Step-by-step explanation:
We need to find the perimeter of the rectangle, given by
P= 2(l+w) where l is the length and w is the width
The units need to be the same
Change 230 yds to ft
230 yd * 3 ft/ y = 690 ft
P = 2(690+200)
P = 2(890)
P =1780
Plsss HELP!!!
*image included
Plan production for the next year. The demand forecast is: spring, 20,600; summer, 9,400; fall, 15,400; winter, 18,400. At the beginning of spring, you have 69 workers and 1,030 units in inventory. The union contract specifies that you may lay off workers only once a year, at the beginning of summer. Also, you may hire new workers only at the end of summer to begin regular work in the fall. The number of workers laid off at the beginning of summer and the number hired at the end of summer should result in planned production levels for summer and fall that equal the demand forecasts for summer and fall, respectively. If demand exceeds supply, use overtime in spring only, which means that backorders could occur in winter. You are given these costs: hiring, $130 per new worker; layoff, $260 per worker laid off; holding, $21 per unit-quarter; backorder cost, $9 per unit; regular time labor, $11 per hour; overtime, $17 per hour. Productivity is 0.5 unit per worker hour, eight hours per day, 50 days per quarter.
Find the total cost of this plan. Note: Hiring expense occurs at beginning of Fall. (Leave no cells blank - be certain to enter "O" wherever required.) Fall 15,400 Winter 18,400 15,400 30,800 77 18,400 36,800 77 Spring Summer Forecast 20,600 9,400 Beginning inventory I 1,030 Production required 9,400 Production hours required 39,140 18,800 Regular workforce 69 47 Regular production Overtime hours Overtime production Total production Ending inventory Ending backorders Workers hired Workers laid off Spring Summer Fall Winter Straight time Overtime Inventory Backorder Hiring Layoff Total Total cost
Can anyone help with problem 5?
Answer:
Other leg: 25 cm
Hypotenuse: 25√2 cm
Step-by-step explanation:
Hi there!
We are given a 45°-45°-90° triangle, and one leg (a side that makes up the right triangle) measures 25 cm
We want to find the length of the other sides
First, let's find the length of the other leg
A 45°-45°90° triangle is actually an isosceles triangle, and if it was to be drawn, the base angles are 45 and 45 degrees
That means the legs of the right triangle are actually the legs in the isosceles triangle as well
So the other leg is also 25 cm
Now, let's find the length of the hypotenuse, which is the side OPPOSITE from the 90° angle
You can solve for the other side using Pythagorean Theorem if you wish, however, there is a shortcut to finding the hypotenuse
In a 45°-45°-90° triangle, if the length of the legs are a, then the hypotenuse is a√2 cm
So that means the length of the hypotenuse in this case is 25√2 cm
Hope this helps!
Question 14 please show ALL STEPS
List of possible integral roots = 1, -1, 2, -2, 3, -3, 6, -6
List of corresponding remainders = 0, -16, -4, 0, 0, 96, 600, 1764
Check out the table below for a more organized way to represent the answer. The x values are the possible roots while the P(x) values are the corresponding remainders.
====================================================
Explanation:
We'll use the rational root theorem. This says that the factors of the last term divide over the factors of the first coefficient to get the list of all possible rational roots.
We'll be dividing factors of 6 over factors of 1. We'll do the plus and minus version of each. Since we're dividing over +1 or -1, this means that we're basically just looking at the plus minus of the factors of 6.
Those factors are: 1, -1, 2, -2, 3, -3, 6, -6
This is the list of possible integral roots.
Basically we list 1,2,3,6 with the negative versions of each value thrown in as well.
---------------------------------
From there, you plug each value into the P(x) function
If we plugged in x = 1, then,
P(x) = x^4 - 3x^3 - 3x^2 + 11x - 6
P(1) = (1)^4 - 3(1)^3 - 3(1)^2 + 11(1) - 6
P(1) = 1 - 3 - 3 + 11 - 6
P(1) = 0
This shows that x = 1 is a root, since we get a remainder 0. Do the same for the other possible rational roots listed above. You should find (through trial and error) that x = -2 and x = 3 are the other two roots.
A sofa is on sale for $703, which is 26% less than the regular price what is the regular price?
If Bob gains 15 pounds, then the ratio of Bob's weight to Tom's weight would be 7 to 5. If Tom weighs 115 pounds, what is Bobs weight now?
Answer:
Step-by-step explana:
-115/5= 23
-23x7=16 1
-161-15=146
Answer:
146 pounds.
Step-by-step explanation:
7 : 5 = 12
? : 115 = ?
115 / 5 = 23
23 x 7 = 161
161 - 15 = 146
The answer is 146.
The terminal side of θ passes through the point (8,−7).
What is the exact value of cosθ in simplified form?
Answer:
8√113 / 113
Step-by-step explanation:
Representing the information on a triangle :
From trigonometry :
Cos θ = Adjacent / hypotenus = AC / AB
AB = hypotenus :
Using Pythagoras :
AB² = AC² + BC²
AB² = 8² + (-7)²
AB² = 64 + 49
AB = √113
Cos θ = AC / AB = 8 / √113
RATIONALIZE :
8/√113 * √113/√113 = 8√113 / 113
Which of the following is a geometric sequence where a1 = 4 and r = 3?
Answer:
4, 12, 36, 108.... continue multiplying by 3
You have a dog-walking business. You charge $12 per hour. Let's define n as the amount you earn and h as the number of
hours you work. You want to make $30, so you figure you need to work 2.5 hours.
Sort the solution methods by whether they are correct or incorrect methods to solve the problem.
Answer:
[tex]n = 12h[/tex]
Step-by-step explanation:
Given
[tex]r = 12/hr[/tex] --- rate
[tex]h \to hours[/tex]
[tex]n \to amount[/tex]
Required
Determine which solution is correct or incorrect
The solutions are not given. So, I will provide a general explanation
The amount (n) is calculated as:
[tex]n = r * h[/tex]
So, we have:
[tex]n = 12 * h[/tex]
[tex]n = 12h[/tex]
The above is the general equation to solve for the amount, given h hours
When h = 2.5, we have:
[tex]n = 12*2.5[/tex]
[tex]n = 30[/tex]
Answer:
going to add a picture
Step-by-step explanation:
:)
Multiply the monomials:
-11x^2y and 0.3x^2y^3
Answer:
-3.3x^4y^4
Step-by-step explanation:
-11x^2y and 0.3x^2y^3
-11x^2y * 0.3x^2y^3
Multiply the constants
-11 * .3 = -3.3
Multiply the x terms
We know that a^b*a^c = a^(b+c)
x^2 * x^2 = x^(2+2) = x^2
Multiply the y terms
y * y^3 = y^(1+3) = y^4
Put them all together
-3.3x^4y^4
You decide to move out of your college's dorms and get an apartment, and you want to discuss the budget with your roommate. You know that your monthly grocery bill will depend on a number of factors, such as whether you are too busy to cook, whether you invite guests for meals frequently, how many special holiday meals you will cook, etc. In particular, G will have an approximate normal distribution with a variance of 2500 and a mean:
μ=300+10M−100B+50H
Where M is the number of meals to which you invite guests, and E[M]=8. B is a measure for how busy you are and assume it is U[0,1]. H is a variable that takes on the value 1 for holiday months of November, December, and January and 0 otherwise.
a. What is the mean of G in a November, where M=10 and B=0.5?
b. What is E(G)?
answer:
a. 400
b. 342.5
Step-by-step explanation:
The mean in this question has been given as
μ=300+10M−100B+50H
where M = 10
B = 0.5
H = 1
we put these into the formula of the mean above
μ=300+10(10)−100(0.5)+50(1)
μ = 300 + 100 - 50 + 50
= 400
So the mean of G in november is = 400
b. We are to find E[G] here
= E[ 300+10M−100B+50H]
m = 8
B = 0.5 or 1/2
h = 1/4
E[ 300+10x8−100x0.5+50*0.25]
= 300+80-50+12.5
= 342.5
the value for E[G] is therefore 342.5
thank you
: Find the value of the trigonometric ratio. Make sure to simplify the If needed
Answer:
24/7
Step-by-step explanation:
tan A = opp/adj
For angle Z, the adjacent leg is 14, and the opposite leg is 48.
tan Z = 48/14
tan Z = 24/7
2. Write the numeral for four thousand and twelve
Find x on this triangle
X is the hypotenuse. Using the given angle and side dimension use the law of sins.
Sin( angle) = opposite leg/ hypotenuse
Sin(30) = 5/2 / x
X = 5/2 / sin(30)
X = 5
The answer is x = 5
write your answer in simplest radical form
9514 1404 393
Answer:
n = 2
Step-by-step explanation:
The ratio of side lengths in a 30°-60°-90° triangle is ...
1 : √3 : 2
We have the ratio ...
n : 2√3 : hypotenuse
from which we can see the basic ratio has been multiplied by 2. That is, n = 2 so the sides of the triangle shown have the ratio ...
2 : 2√3 : 4
