The formula for simple interest is the following:
[tex]S=Prt[/tex]
In this formula, [tex]S[/tex] is the amount of interest, [tex]P[/tex] is the principal (or initial) amount, [tex]r[/tex] is the interest rate, and [tex]t[/tex] is the length f time, typically in years.
First, let's make a couple of changes to how we wrote down the variables.
Change the interest rate, [tex]6\%[/tex], to the decimal value [tex]0.06[/tex].Convert the length of time to years. 180 days divided by 360 days per year equals [tex]0.5[/tex] years.Substitute in the values and solve with a calculator.
[tex]\begin{aligned}S&=16,500\cdot0.06\cdot0.5\\&=\boxed{495}\end{aligned}[/tex]
A retail store in Des Moines, Iowa, receives shipments of a particular product from Kansas City and Minneapolis. Let x = number of units of the product received from Kansas City y = number of units of the product received from Minneapolis a. Write an expression for the total number of units of the product received by the retail store in Des Moines. b. Shipments from Kansas City cost $0.20 per unit, and shipments from Minneapolis cost $0.25 per unit. Develop an objective function representing the total cost of shipments to Des Moines. c. Assuming the monthly demand at the retail store is 5000 units, develop a constraint that requires 5000 units to be shipped to Des Moines. d. No more than 4000 units can be shipped from Kansas City, and no more than 3000 units can be shipped from Minneapolis in a month. Develop constraints to model this situation. e. Of course, negative amounts cannot be shipped. Combine the objective function and constraints developed to state a mathematical model for satisfying the demand at the Des Moines retail store at minimum cost. Solve using linear programming
The expression for the total number of units of the product received is x + y.
How to depict the information?The total will be =y+x because it will be the sum of the two shipment quantities.
b. Cost = $.20(x)+$.25(y) because the cost will be the sum of the costs per unit for each shipment.
c. 5000 =x+y allows for any combination of x and y units.
d. Total will be: x+y where x<=4000 and y<=3000
e. The minimum cost is where a and b are minimized in demand =ax+by. We cannot determine a maximum value for a or b because we do not know what the demand is. If the problem calls for referral to part b, then use the equation demand=$.20x
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- 10
-5
A
B
10-
8-
6-
4-
-4-
-6-
-8
-10
D
5
C
10
Which coordinates below would form the
image of the triangle above if the center
of dilation is at point D and the scale
factor is 2?
O A'(-7, 8), B'(-5, -2), C'(7, -2)
O A'(-6, 6), B'(-4, -4), C'(8, -4)
O A'(-11, 13), B'(-8, -2), C'(10, -2)
O A'(-1, 0.5), B'(-0.5, -2), C'(2.5, -2)
Answer:
HDUEHD ehvd to be a great day of school and I have a great day of school andmath
look at the picture
Answer:
logarithmic
Step-by-step explanation:
I'm jujust that good to help you
evaluate if a= 28 and b= -3 a/4+b
Answer:
4
Step-by-step explanation:
divide the numbers
subtract the numbers
final answer:
= 4
When the function f(x) = 8* is evaluated for x = 2, the output is:
O 64.
O 10.
16.
Answer:
[tex]\huge\boxed{\sf 64}[/tex]
Step-by-step explanation:
Given function:[tex]f(x) = 8^x[/tex]
Put x = 2
[tex]f(2) = 8^2\\\\f(2) = 8 \times 8\\\\f(2) = 64\\\\\rule[225]{225}{2}[/tex]
If f(x) = x^3 and g(x) = -2x^3, how has f(x) been transformed to get g(x)?
The transformation that is applied to f(x) to get g(x) is that the function f(x) is vertically stretched by a factor of -2.
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units, y=f(x+c) (same output, but c units earlier)Right shift by c units, y=f(x-c)(same output, but c units late)Vertical shift
Up by d units: y = f(x) + dDown by d units: y = f(x) - dStretching:
Vertical stretch by a factor k: y = k × f(x)Horizontal stretch by a factor k: y = f(x/k)If f(x) = x³ and g(x) = -2x³, then the transformation that is applied to f(x) to get g(x) is that the function f(x) is vertically stretched by a factor of -2.
Hence, the transformation that is applied to f(x) to get g(x) is that the function f(x) is vertically stretched by a factor of -2.
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It would take 15men 8days to dig a trench of 240metres long.How many days would it take 18men to dig a trench of 360meters long working at the same Rate.
Using proportions, it is found that it would take 6.4 days for 8 men to dig a trench of 360 meters long working at the same rate.
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, the rule of three is given as follows:
8 days - 15 men - 240 meters
x days - 18 men - 360 meters
The number of men is inverse proportional to the number of days, hence we divide 18 by 15 instead of 15 by 18, then:
[tex]\frac{8}{x} = \frac{18}{15} \times \frac{24}{36}[/tex]
[tex]\frac{8}{x} = \frac{6}{5} \times \frac{4}{6}[/tex]
[tex]\frac{8}{x} = \frac{5}{4}[/tex]
Applying cross multiplication:
5x = 32.
x = 32/5
x = 6.4 days.
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If IK=JK, find mlJ
A. 72°
B. 82°
C. 122°
D. 134°
Answer:
D.134
Step-by-step explanation:
what is the remainder of 2x^3-12x^2+11x+2 divided by x-5
Answer:
7
Step-by-step explanation:
When x = 5, 2x³ - 12x² + 11x + 2 = 7.
A credit card company charges a 4% balance transfer fee. If you want to transfer a balance of $2,100 to this credit card, what fee would you pay?
Answer:
$84
Step-by-step explanation:
So since it charges 4%, this means you need to find 4% of what you're transferring. To find x% of a number, you need to convert the percentage to a decimal, and then multiply it by the number you're trying to find x% of. So in this case 4%/100 = 0.04. Now take this decimal and multiply it by 2100, and this will give you 84. So the fee would be $84
Answer:
$84
Step-by-step explanation:
= 4% × $2100
= 0.04 × $2100
= $84
What is this math problem in Simply form 3-4(-2-7)
1. make sure you understand what the problem really is
3-4(-2-7)
= 3 + -4 × (-2 + -7)
2. always begin with the brakes
3 + -4 × (-2 + -7)
= 3 + -4 × (-9)
3. then ² and [tex] \sqrt{?} [/tex]
4. then × and and ÷
3 + -4 × (-9)
= 3 + 36
5. lastly + and -
3+36
=39
O Both x and y are positive.
O Both x and y are negative.
Ox is positive, and y is negative.
Ox is negative, and y is positive.
The point P(x, y) lies on the terminal side of an angle = -60° in standard position. What are the signs of the values
of x and y?
The value of x has a positive sign and the value of y has a negative sign. Option C
What is a unit circle?An angle in the unit circle of angle α with a radius of 1 with the set of points;
cos α and sin α
In the given problem, we have the angle as -60º, which is equal to an angle of 360 - 60 to give us 300º
Also, it is in the fourth quadrant, where the cosine is positive and the sine is negative.
Thus, the value of x has a positive sign and the value of y has a negative sign.
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Your original grades on your exams were: 75, 85, 90, 90, 100, 75, 80, 100, 90. You retake the exams and now your scores are: 85, 85, 100, 90, 100, 85, 80, 100, 90. By how many percentage points did you improve your average score?
Answer:
Your average improved by 13 [tex]\frac{1}{3}[/tex] %.
Step-by-step explanation:
First set:
(75 + 85 + 90 + 90 + 100 + 75 + 80 + 100 + 90) ÷ 9 = 77 [tex]\frac{2}{9\\}[/tex] %
Second set:
(85 + 85 + 100 + 90 + 100 + 85 + 80 + 100 + 90) ÷ 9 = 90 [tex]\frac{5}{9}[/tex] %
Improvement:
90 [tex]\frac{5}{9}[/tex] % - 77 [tex]\frac{2}{9\\}[/tex] % = 13 [tex]\frac{1}{3}[/tex] %
round the answer to the nearest
By knowing the blood pressure and applying the quadratic formula, the age of a man whose normal blood pressure is 129 mm Hg is 40 years old.
How to use quadratic equations to determine the age of a man in terms of blood pressure
In this problem we have a quadratic function that models the blood pressure as a function of age. As the latter is known, we must use the quadratic formula to determine the former:
129 = 0.006 · A² - 0.02 ·A + 120
0.006 · A² - 0.02 · A - 9 = 0
[tex]A = \frac{0.02 \pm \sqrt{0.006^{2}-4\cdot (0.006)\cdot (- 9)}}{2\cdot (0.006)}[/tex]
A = 1.667 + 38.733
A = 40
By knowing the blood pressure and applying the quadratic formula, the age of a man whose normal blood pressure is 129 mm Hg is 40 years old.
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If the sides of a polygon are x + 3 units, 2x – 4 units, 5x units, and 7x + 8 units, then find the perimeter of the polygon.
Answer:
The answer is 15x + 7
Step-by-step explanation:
Since the perimeter of a REGULAR polygon is the number of sides multiplied by the length, and the lengths of the sides are all different, it can be assumed that this is an irregular polygon. That means the formula to find the perimeter changes to all the sides added together.
1 x + 3
2 x - 4
5 x + 0
+ 7 x + 8
15 x + 7
In the figure above ac bisects bcd. what is the length of cd?
In the the figure above AC bisects BCD in the quadrilateral, the length of CD will be 6cm.
How to calculate the value?It should be noted that the longer diagonal is a perpendicular bisector of the shorter diagonal.
From the diagram given, the value of AD is 6cm. Therefore, according to the angle bisector theorem, the value of CD is 6cm as they're congruent.
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The position of an object at time t is given by s(t) = 1 - 12t. Find the instantaneous velocity at t = 2 by finding the derivative.
The change of displacement with respect to time is defined as speed. Velocity is a vector quantity. The instantaneous velocity at t = 2 is -12.
What is velocity?The change of displacement with respect to time is defined as Velocity. velocity is a vector quantity. It is a time-based component. Its standard unit is m/sec.
Given that the position of an object at time t is given by s(t) = 1 - 12t. Therefore, the velocity of the object can be written as,
V = ds/dt
= d(1 - 12t)/dt
= -12
s'(t) = -12
Now, the instantaneous velocity at t=2 is,
s'(2) = -12
Hence, the instantaneous velocity at t = 2 is -12.
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How do I calculate the 2nd question?
(Attached the file)
Answer:
0.29287
Step-by-step explanation:
You want to use the binomial cumulative distribution function (binomcdf). The purpose of this function is that it allows you to obtain the probability of observing less than or equal to x successes in n trials, with the probability p of success on a single trial.
x in this case is 182, n is 200, and p is 0.9005. Essentially by inputting these values, we find the probability that out of 200 passengers with a 0.9005 chance of getting on the plane, that 182 or less show up.
This gives us P(x <= 182) = 0.70713. (You need your calculator for this step, input the values above in the binomcdf function)
We want to find the probability of more than 182 passengers showing up though, so it would be 1 - 0.70713 = 0.29287.
Thus the probability that when 200 reservations are accepted for the flight, there are more passengers than seats available is 0.29287.
I need the answer pls, any of y'all's answers would help!
Answer:
1
Step-by-step explanation:
The differences in the values on each spot on the line is 2, because -5 is in between -7 and -3. Going to the right means that the values are increasing. We go from -7, to -5, to -3, to -1, and finally, to 1.
Brainliest, please :)
Select the correct answer.
Three corporations each own land. Corporation A owns 3.2 × 105 acres, corporation B owns 4 × 104 acres, and corporation C owns 4.3 × 105 acres. Which corporation owns the most land? How many times greater is corporation A’s land than corporation B’s land?
A
Corporation A owns the most land. Corporation A owns 8 times more land than corporation B.
B.
Corporation B owns the most land. Corporation A owns 4 times more land than corporation B.
C.
Corporation C owns the most land. Corporation A owns 8 times more land than corporation B.
D.
Corporation C owns the most land. Corporation A owns 80 times more land than corporation B.
E.
Corporation A owns the most land. Corporation A owns 40 times more land than corporation B.
Using scientific notation, the correct statement is given by:
C. Corporation C owns the most land. Corporation A owns 8 times more land than corporation B.
What is scientific notation?A number in scientific notation is given by:
[tex]a \times 10^b[/tex]
With the base being [tex]a \in [1, 10)[/tex].
Considering the amounts in scientific notation, the standard amounts in acres of each corporation are given as follows:
Corporation A: [tex]3.2 \times 10^5 = 320000 = 320,000[/tex].Corporation B: [tex]4 \times 10^4 = 40000 = 40,000[/tex].Corporation C: [tex]4.3 \times 10^5 = 430000 = 430,000[/tex].Hence corporation C owns the most land. 320,000/40,000 = 8, hence Corporation A owns 8 times more land than corporation B, and statement C is correct.
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what is the independent variable of "i did 60 brush strokes in 1 minute"
The independent variable is brush strokes
How to determine the independent variable?The statement is given as:
"I did 60 brush strokes in 1 minute"
The independent variable is the action that is done.
From the statement.
The action is the strokes of brush
Hence, the independent variable is brush strokes
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Laura opened a deposit account. In the first month, she made an initial deposit of $2500. She plans to contribute $225 a month after her initial deposit. The account does not pay any interest.
After how many months will she have a total of $6,775?
A. 18
B. 15
C. 20
D. 21
Answer:
20 months
Turn sentences into equation:
She deposits $225 every month after initial deposit of $2500 in first month
Equation: y = 2500 + (x - 1)225
where y represents total amount, x represents months
Use this equation to find at which month her account will have $6,775
2500 + (x - 1)225 = 6,775
(x - 1)225 = 6,775 - 2,500
(x - 1)225 = 4275
x - 1 = 19
x = 20
Thus, it will take 20 months when she have a total of $6,775.
DECIDE WHEATHER THE ORDER PAIR(-3,-5) IS A SOLITION OF THE EQUATION 7X-5Y=15
Answer:
(-3, -5) is not a solution of the equation 7x - 5y = 15
Step-by-step explanation:
1) Knowing that coordinates are given to us as (x, y), plug in the ordered pair into the equation. [tex]7(-3)-5(-5)=15[/tex]
2) Do PEMDAS on the left side of the equation
[tex]-21+25=15[/tex][tex]4=15[/tex][tex]4\neq 15[/tex]Answer:
Not a solution
Step-by-step explanation:
Hello!
We can determine if it's a solution by plugging in the x and y-values of the point into the equation. If both sides are equal to each other, then it is a solution.
-3 is the x-value and -5 is the y-value, since an ordered pari is written in the form of (x,y).
Evaluate7x - 5y = 157(-3) - 5(-5) = 15-21 + 25 = 154 ≠ 15Since both sides are not equal to each other, (-3,-5) is not a solution.
solve for x -
[tex]\bold{x {}^{2} - 25 + 16 = 0}[/tex]
ty! ~
Hey!
Your equation is -
[tex]x {}^{2} - 25 + 16 = 0[/tex]
[tex]x {}^{2} - 9 = 0[/tex]
We can write 9 as 3² (Why?) because it forms identity a² - b² = (a + b) (a - b) .
[tex]x {}^{2} - {3}^{2} = 0[/tex]
[tex](x - 3)(x + 3) = 0[/tex]
This gives the information that either,
x - 3 = 0 or x + 3 = 0
So, x = 3 or x = -3
Hope it helps, you may ask if you have any confusions ^-^
Answer:
x = 3, x = -3
Step-by-step explanation:
x² - 25 + 16 = 0
⇒ x² - 9 = 0
• Add 9 to both sides:
⇒ x² = 9
• Square root both sides of equation:
x = [tex]\sqrt{9}[/tex]
x = ± 3
x = 3 and x = -3
y-7 = (12-x)2 in vertex form
Answer:
y = -2x + 31
Step-by-step explanation:
Vertex form a parabola refers to a place or a point where it turns. It takes the form of;
y = mx + c
From our question, we are supposed to convert the equation y-7 = (12-x)2 into vertex form.
To begin, open the brackets on the RHS;
y - 7 = 24 - 2x.
Then move -7 to the RHS which becomes the positive.
Y = 24 - 2x + 7
= 31 - 2x
Convert it to the form y = mx + c.
y = -2x + 31
This is the vertex form, y = -2x + 31.
Note:
For a standard form/quadratic, the equation has to be in the form ax² + bx + c = ya washer and dryer costs $745 combined the washer costs $45 more than the dryer how much does the dryer cost
The triangles shown below must be congruent.
Answer:
Yes, they are congruent
Step-by-step explanation:
The triangles are congruent as they follow the ASA rule or, Angle Side Angle.
All the angles AND sides are corresponding, so they are congruent.
Hope this helped (:
20. Find the solution to the system of linear equations below:
x - 3y = -5
2x + 5y = 12
O (-5, 12)
O (3,2)
O (-2,7)
O (1,2)
Answer:
(1, 2)
Step-by-step explanation:
So you can solve this systems of equations by substitution. Substitution involves "finding" the value of one of the variables and then substituting that into the other equation
In this example I'll try to define an equation equal to that of "2x" using the first equation and then substitute that into the second equation
Given:
[tex]x-3y=-5[/tex]
Add 3y to both sides
[tex]x=3y-5[/tex]
Multiply both sides by 2
[tex]2x = 6y-10[/tex]
Given:
[tex]2x+5y=12[/tex]
Substitute 2x as (6y-10)
[tex](6y-10)+5y=12[/tex]
Simplify
[tex]11y-10=12[/tex]
Add 10 to both sides
[tex]11y = 22[/tex]
Divide both sides by 11
[tex]y=2[/tex]
Plug 2 in as y (works for either given equation)
[tex]x-3(2)=-5[/tex]
simplify
[tex]x-6=-5[/tex]
add 6 to both sieds
x=1
When a is divided by 7, the remainder is 5; and when b is divided by 7, the remainder is 4. What is the remainder when a + b is divided by 7? When a is divided by 7 , the remainder is 5 ; and when b is divided by 7 , the remainder is 4. What is the remainder when a + b is divided by 7 ?
Answer:
9
Step-by-step explanation:
35(a) / 7 = 5
28(b) / 7 = 4
a + b = 35 + 28
35 + 28 = 63
63 / 7
= 9
Hope that helps! :)
2 over 6 = Y over 9 Fraction equation is required
Answer:
y = 3Step-by-step explanation:
2 over 6 = Y over 9 Fraction equation is required
2/6 = y/9
y = 2/6 * 9
y = 3
check
2/6 = 3/9
1/3 = 1/3
the answer is good