Using simple interest, the amounts she invested are given as follows:
$3,000 at 9%.$1,500 at 6%.Simple InterestSimple interest is used when there is a single compounding per time period, usually measured in years.
The amount of money after t periods in is modeled by:
A(t) = P(1 + rt)
The interest accrued after t periods is modeled by:
I(t) = Prt
In which:
P is the initial amount.r is the interest rate, as a decimal.She had two investments, investing a total of $4500, hence:
[tex]P_1 + P_2 = 4500[/tex]
The return for the 9% investment exceeds that from the 6% investment by $180, hence:
[tex]I_2 = 0.06(4500 - P_1)[/tex][tex]I_1 = 0.09P_1[/tex][tex]I_2 = I_1 - 180[/tex]Then:
[tex]I_2 = 0.06(4500 - P_1)[/tex]
[tex]I_1 - 180 = 0.06(4500 - P_1)[/tex]
[tex]0.09P_1 - 180 = 0.06(4500 - P_1)[/tex]
[tex]0.15P_1 = 450[/tex]
[tex]P_1 = \frac{450}{0.15}[/tex]
[tex]P_1 = 3000[/tex]
Which is the amount invested at 9%, hence the amount invested at 6%, considering that a total of $4,500 was invested, is given by:
4500 - 3000 = $1,500.
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PLS HELP!! 20 POINTS ASAP
18 5/12+ 8 10/17 + 23 7/12 + 28 7/17
Answer:
79
Step-by-step explanation:
same thing as 79/1
HELP WITH 1 AND 2 PLEASE 20 POINTS AND BRAINLIEST SHOW YOUR WORK!!!!!!
1. The least number of hours that.Kee can work is 7 hours.
2. The maximum number of miles that Julie will drive will be 272 miles.
How to illustrate the information?1. Lee makes $64 per hour and he wants to make no less than $400 each hours for the trip. The number of hours will be:
Let the number of hours = h
64h >= 400
Divide
h >= 400/64
h >= 6.25
The least hour should be 7 hours.
2. The maximum number of miles that Julie will drive will be:
44(3) + 0.25m = 200
m = number of miles
132 + 0.25m = 200
0.25m = 200 - 132
0.25m = 68
m = 68 / 0.25
= 272
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Help me please
15+ points
The equation is y=5x+16.
How to form the required equation?The formula y=mx+b is expressed in slope-intercept form. We are aware of the slope (m) as well as a point (-2,6). We now require the y-intercept (b).We need to enter the information we are aware of in order to solve the y-intercept (b).Y = 6, M = 5, and X = -2 are known values. The equation must be like this: 6=5(-2)+bContinuing, 5(-2) is just 5 times -2, or -10. The new formula is 6=-10+b.Since we must repeat this process for both sides, we must add 10 to the right side to cancel it out and 10 to the left to obtain b. 6+10=-10+10+bB must therefore be 16 because of this.The last step is to construct the equation, where all that is required is to correct the values of m and b in the slope-intercept equation y=mx+b. We know that m is 5 and b is 16.y - 6 = 5(x - (-2)) y=5x+16Therefore, y=5x+16 is the solution.To learn more about equations, refer
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If f(x) = -x³ + x² + x, find f(-3)
Use the properties of equality to solve each equation r + 18 = 26
To solve this equatio you use the next property:
Subtraction Equal Property: it is used in expressions with adds. State that you can substract the same amount from both sides of the equation and maintain euality.
In this case, to solve r you substract 18 in both sides of the equation:
[tex]r+18-18=26-18[/tex]As 18-18 is 0;
[tex]r=8[/tex]Then, The solution of r+18=26 is r=8how to solve this one
Need help, please.Quick answer is okay
xplanation:
Step 1. e are given the following zeros of a polynomial function.
- 1 with a multiplicity of two, which means that is a zero two times:
[tex]\begin{gathered} x_1=1 \\ x_2=1 \end{gathered}[/tex]and the other two zeros are:
[tex]\begin{gathered} x_3=2+\sqrt{2} \\ x_4=2-\sqrt{2} \end{gathered}[/tex]And we need to find the equation that has these four zeros.
tep 2. 2R
[tex]f(x)=(x-x_1)(x-x_2)(x-x_3)(x-x_4)[/tex]tep 3. S
[tex]f(x)=(x-1)(x-1)(x-(2+\sqrt{2}))(x-(2-\sqrt{2}))[/tex]tep 4. S
[tex]f(x)=(x-1)(x-1)(x-2-\sqrt{2})(x-2+\sqrt{2})[/tex]tep 5. T
[tex]f(x)=(x^2-2x+1)(x-2-\sqrt{2})(x-2+\sqrt{2})[/tex]Then, let's multiply the second and third parentheses:
[tex]f(x)=(x^2-2x+1)(x^2-2x+x\sqrt{2}-2x+4-2\sqrt{2}-x\sqrt{2}+2\sqrt{2}-2)[/tex]Multiple terms cancel and the result is:
[tex]f(x)=(x^2-2x+1)(x^2-4x+2)[/tex]tep 6. TT
[tex]f(x)=x^4-4x^3+2x^2-2x^3+8x^2-4x+x^2-4x+2[/tex]Combining like terms:
[tex]f(x)=x^4-6x^3+11x^2-8x+2[/tex]This is shown in option D.
Answer:
D
[tex]f(x)=x^4-6x^3+11x^2-8x+2[/tex]please solve this question
We have a random variable, the time it takes to wash the dishes, that is uniformly distributed between 7 minutes and 16 minutes.
We have to calculate the probability that this random variable will have a value between 11 and 15 minutes.
We can calculate this probability as:
[tex]P(11Answer: the probability is 0.44.Hi I need help on my homework only number 1
) Let us assume that the interest was compounded annually. The formula for calculating compound interest is expressed as
A = P(1 + r/n)^nt
where
A is the amount after t years
P is the principal or initial amount invested
r is the interest rate
n is the number of compounding periods in a year
t is the number of years
From the information given,
P = 130
r = 4% = 4/100 = 0.04
n = 1 because it was compounded once in a year
t = 10
By substituting the values into the formula, we have
A = 130(1 + 0.04/1)^1 * 10
A = 130(1.04)^10
A = 192.43
Rounding to the nearest whole number, the amount after 10 years is $192
use this equation to write an equation that has many /infinite solutions, no solution one solution y =3x + 4
the initial expression is:
[tex]y=3x+4[/tex]So this equation has already one solution
Now if we want to have infinit solution we an rest 3x so:
[tex]\begin{gathered} y=3x-3x+4 \\ y=4 \end{gathered}[/tex]So x can have any value, so there are infinit solutions
And to have no solutions we can add 5 -y at the left an
please help thank you
Simplify fully the following
2√5 × 5√5
2√3 x 3√8
Hey I really need help on this question
We have
[tex]9x+5y-10[/tex]We will substitute the values given
x=6 y=1
[tex]9(6)+5(1)-10[/tex]we solve the operations in order to obtain the result
[tex]54+5-10=49[/tex]the answer is 49
What are the order pairs for y=2/5x?(14,35)(30,1250,2010,440,2425, 5/2
Ok
y = 2/5x
ok
a) y = 2/5(14)
y = 28/5
y = 5.6 the first one is not an order pair
b) y = 2(30)/5
y = 60/5
y = 12 the second one is an order pair
c) y = 2/5(50)
y = 100/5
y = 20 the third one is an order pair
d) y = 2/5(10)
y = 20/5
y = 4 the four one is an order pair
e) y = 2/5(40)
y = 80/5
y = 16 the fifth one is not an order pair
f) y = 2/5(25)
y = 50/5
y = 10 the sixth one is not an order pair.
The solutions are (30, 12), (50, 20) and (10, 4)
Factor completely
4v6+18v5-10v4
Answer:
[tex]2v^4 (v+5)(2v-1)[/tex]
Step-by-step explanation:
[tex]4v^6+18v^5-10v^4 \\ \\ =2v^4 (2v^2 + 9v-5) \\ \\ =2v^4 (v+5)(2v-1)[/tex]
step by step explanations for the following
g(x)=4x-5
f(x)= -2x-3
find (f•g) (-8)
and problems on the paper numbers 5-8 please
Answer:
5. [tex]\bold{(g \circ f)(-3) = 16}}[/tex]
6. [tex]\bold{h(h(-3x)) = -12x + 15 }}[/tex]
7. [tex]{\bold{f\left(g\left(x-3\right)\right):\quad 3x-21}}[/tex]
8. [tex]\bold{\text \bold g(f(-3x)) = -36x + 15}}[/tex]
Step-by-step explanation:
These are examples of composite functions.
What is a composite function?
A function by definition is a process that takes a collection of inputs and produces a corresponding collection of outputs in such a way that the process produces one and only one output value for any single input value.
Since we consider a function a process it makes sense to think of two functions acting in sequence to produce a single output. The output from one function is fed into the second function.
A composite function can be written as:Note that we can have [tex]f[/tex][tex]g[/tex] as the outer function, in which case the notation will be [tex](g \circ f)(x)[/tex] or [tex]g(f(x))[/tex]
Problem Solution
5. [tex]g(x) = x + 3 \;\text and\; f(x) = 3x + 4[/tex]
Find [tex](g \circ f)(-3) = g(f(-3))[/tex]
6. [tex]h(x) = 2x + 5[/tex]
Find [tex]h(h(-3x))[/tex]
[tex]7.\;\;\;g\left(x\right)\:=\:x-\:3,\:f\left(x\right)\:=\:3x\:-\:3\\\\\text{Find } \:f\left(g\left(x-3\right)\right)[/tex]
[tex]\mathrm{For}\:g=x-3\:\mathrm{substitute}\:x\:\mathrm{with}\:x-3[/tex].[tex]\bold{8.\;\;g(x) = 3x + 3, f(x) = 4x + 4}\\\\\bold{\text{Find } g(f(-3x))}[/tex]
[tex]\text {For}\:f(x) =4x+4\:\mathrm{substitute}\:x\:\mathrm{with}\:-3x}[/tex]Line segments JK and JL in the xy-coordinate plane both have a common endpoint /(-4, 11) andmidpoints at M, (2,16) and M, (-3, 5), respectively.What is the distance between M, and M.? Round to the nearest tenth
SOLUTION
From the question, since the coordinates of the mid-points JK and JL has been given as M (2,16) and M, (-3, 5), respectively.
To find the distance between these two mid-points, we simply use the distance formula to do that.
The distance formula is given as
[tex]\begin{gathered} d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ where\text{ d is the distance } \end{gathered}[/tex]Applying these to the points M (2,16) and M, (-3, 5), we have
[tex]\begin{gathered} d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ d=\sqrt{(-3-2)^2+(5-16)^2} \\ d=\sqrt{(-5)^2+(-11)^2} \\ d=\sqrt{25+121} \\ d=\sqrt{146} \\ d=12.083045 \\ d=12.1\text{ units } \end{gathered}[/tex]Hence the answer is 12.1 units
56 a) -1 < x < 6
d) 7,1
b) x > 0,4
2
e) x ≤
7
c) 3,9 < x
f) x ≥ 5
Answer:
a) -1< x < 6
Step-by-step explanation:
you no. how true answer
Find the width w
184 = 2w + 64 + 2w
Answer:
the aswer is 30 glad i could help
Step-by-step explanation:
Answer:
w = 30
Step-by-step explanation:
184 = 2w + 64 + 2w
(2w + 2w)
184 = 4w + 64
(184 - 64)
120 = 4w
(÷4)
w = 30
1. The total number of pancakes that can be made for a pancake breakfast fundraiser is directly related to the
amount of batter that is available. If 28 cups of batter make 112 pancakes, then which of the following is
closest to the number of pancakes that can be made with 45.4 cups of batter?
If we have 45.4 cups of batter, we can make 181 pancakes using unitary method.
What is unitary method?The unitary approach is a technique for problem-solving that involves first calculating the value of a single unit, then multiplying that value to figure out the required value.
Given Data
28 cups of batter to make 112 pancakes
To make 1 unit
28 cups of batter = 112 pancakes
1 cup of batter = 4 pancakes
If we have 45.4 cups of batter, we can make,
1 cup of batter = 4 pancakes
45.4 cup of batter = 45.4(4)
45.4 cup of batter = 181 pancakes ( approximately )
If we have 45.4 cups of batter, we can make 181 pancakes using unitary method.
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find the slope of the line that passes through (-82, -26) and (-81, 4)
PROBLEM
Slope of a line passes through (-82,-26) and (-81,4)
Method
Step 1
Write out slope formula
[tex]\text{Slope = }\frac{y_2-y_1}{x_2-x_1}[/tex]Step 2
write out all parameters
x1 = -82, y1 = -26
x2 = -81 , y2 = 4
Step 3
Input all parameter
[tex]\begin{gathered} \text{Slope = }\frac{4\text{ - (-26)}}{-81\text{ - }(-82)} \\ \text{Slope = }\frac{4\text{ + 26}}{-81+82} \\ \text{Slope = }\frac{30}{1} \\ \\ \text{Slope = 30} \end{gathered}[/tex]what is the answer to -6 2/5 + 7/3
Question
Simplify the expression:
(4/9)^3
Answer:
Step-by-step explanation:
(4^3/(9^3)
= 64/729 or0.09
how do i solve this
We are basically asked to perform the product of expressions that contain complex numbers a s roots of polynomials. So it is essential to identify the complex root in order to facilitate our products that otherwise could be really time consuming.
First product:
(x + 3 + 5i) (x + 3 - 5i) we are going to write as: ((x +3) +5i) ((x+3) - 5i). So this is going to be interpreted as a difference of squares (a + b) ( a - b) = a^2 - b^2:
((x +3) +5i) ((x+3) - 5i) = (x+3)^2 - (5i)^2 = (x+3)^2 - (-25) = (x+3)^2 + 25
We are using the fact that (i)^2 = -1 to convert - 25 (i)^2 = + 25
Now we solve the square of the binomial (x+3) , that is:
(x+ 3)^2 = x^2 + 6x + 9
Now this combined with + 25 gives: x^2 + 6x + 34 This is one of the options in blue background shown at the tops (the fourth one starting from the left)
Second product:
(x - 4i) (x + 4i) which is an easirer product than the one above because we can solve it just using difference of squares: (a - b) (a + b) = a^2 - b^2:
(x - 4i) (x + 4i) = x^2 - (4i)^2 = x^2 - 16 (i)^2 = x^2 +16
This is the second expression in blue background from left to right.
Third product:
(x - 6 + i) (x - 6 - i) for which we apply the same technique as in the first product we solve above:
(x - 6 + i) (x - 6 - i) = ((x - 6) + i) ((x - 6) - i) = (x-6)^2 - (i)^2 = (x-6)^2 - (-1) = (x-6)^2 + 1 = x^2 - 12 x + 36 + 1 = x^2 - 12 x + 37 which is the very first expression in blue background in the image you uploaded.
Olease move the bue background boxes so as to match the indicated products.
What is −12÷2/3?
Responses
−36
−24
−18
−8
Question 4
Two diagonally opposite vertices of a square on a coordinate grid are located at (-5,7). (1,1). What is the
perimeter of the square? (7.G.6)
1p
Check the picture below.
A population that consists of 500 observations has a mean of 40 and a standard deviation of 15. A sample of size 100 is taken at random from this population. Assume this is an infinite population. What is the standard error of the sample mean?
The standard error of the sample nean for a population that consists of 500 observations is 1.5
How to calculate the sample mean?From the information, the population that consists of 500 observations has a mean of 40 and a standard deviation of 15.
It should be noted that the sample mean is calculated as:
= Standard deviation / ✓number
= 15 / ✓100
= 15 / 10
= 1.5
Therefore, the standard error is 1.5.
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Let f be the function given by f(x)=∣∣x2−2∣∣(x+0.4)(x2−2)(x+0.4). On which of the following open intervals is f continuous?
Using the continuity concept, it is found that the function is continuous on the following interval:
C. (0, 1).
What is the continuity concept?A function f(x) is continuous at x = a if it is defined at x = a, and the lateral limits are equal, that is:
[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]
In the context of this problem, the numeric values are especially relevant, as the function not continuous at the zeros of the denominator.
The denominator of the function is given as follows:
(x² - 2)(x + 0.4).
Hence the discontinuity points are:
x² - 2 = 0 -> x = -1.41 and x = 1.41.x + 0.4 = 0 -> x = -0.4.Hence the only interval in which the function is continuous over the entire interval is given by option C.
What is the missing information?The function and the possible options are given by the image at the end of the answer.
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A dinner theater charges $20 per person. Your table can hold a maximum of five people. Does the situation represent a function?
If so, find the domain and range. If not, leave this blank.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Domain: Response area
Range: Response area
The situation represents a function, while the domain and the range are 0 <= x <= 5 and 0 <= y <= 100, respectively
How to determine if the situation is a function?From the question, we have
Charges = $20 per person
Let the number of people be x and the total charges be y
So, we have
y = 20x
The above equation is a linear function
The domain and the rangeFrom the question, we have
Total number of people per seat = 5
So, the domain is 0 <= x <= 5
Substitute 5 for x in y = 20x
y = 20 x 5
Evaluate
y = 100
So, the range is 0 <= y <= 100
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write the expression as a power and evaluate it. 16*32
The expression as power [tex]16^{3/2}[/tex] is 64.
What are exponents and power?Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner.
Given:
[tex]16^{3/2}[/tex]
using law of exponent
[tex]x^{(a * b)} = (x^a)^b[/tex]
Now, splitting 16 as 4 square
[tex]16^{3/2}[/tex]
=(4²[tex])^{3/2}[/tex]
=4³
=4 x 4 x 4
=64
Hence, expression as power [tex]16^{3/2}[/tex] is 64.
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Answer: 16^2.25
This is the correct answer thanks