[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$500\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &5 \end{cases} \\\\\\ A=500\left(1+\frac{0.04}{4}\right)^{4\cdot 5} \implies A=500(1.01)^{20}\implies A \approx 610.10[/tex]
Linear Equations Word Problems
Sasha spent half of her allowance going to the movies. She washed the family car and earned $6. What is her weekly allowance if she ended with $15?
Answer:
Her weekly allowance is $18
Step-by-step explanation:
We can use an algebraic equation to solve this problem.
x/2 + 6 = 15
x/2 + 6 ( - 6) = 15 ( - 6)
x/2 ( · 2)= 9 ( · 2)
x = 18
Her weekly allowance is $18
Help me and please explain your answer Act smart
The only equation that represents a piecewise defined function is;
Option A: f(x) = {-2, if x ≥ 4
{x², if x < 4
What is a piecewise function?A piecewise function is defined as a function that consists of multiple subfunctions, whereby each subfunction defined over a specific subset of the domain of the main function which is called a subdomain.
The equation of a piecewise function is usually written with a curly bracket that indicates the fact of being comprised of more than one subfunction. An example of a piecewise function is;
f(x) = {x, x < 0
{x + 1, x ≥ 0
Let us look at each of the given functions;
Function in option A is clearly a piecewise function when compared to the definition given above
Read more about Piecewise Functions at; https://brainly.com/question/27262465
#SPJ1
Which equation represents a line that has a slope of One-third and passes through point (–2, 1)?
y = one-third x minus 1
y = one-third x + five-thirds
y = one-third x minus five-thirds
The equation of the line with a slope of one third and passes through (-2, 1) is y = one-third x + five-thirds.
How to find the equation of a line?The equation of a line can be represented in a slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the equation of the line has a slope of 1 / 3. Let's find the y-intercept using the coordinates (-2, 1)
y = 1 / 3 x + b
1 = 1 / 3 (-2) + b
1 + 2 / 3 = b
b = 3 + 2 / 3
b = 5 / 3
Therefore, the equation is y = 1 / 3 x + 5 / 3
learn more on equation of a line here: https://brainly.com/question/14200719
#SPJ1
What is the radical form of each of the given expressions?
Drag the answer into the box to correctly match each expression.
Answer:
The answer is displayed in the attached image.
Step-by-step explanation:
To find the radical form of an expression, first determine what is in the denominator of the fractional exponent. That number will determine the order of the root you will take. The numerator will be the power of your original number
EXAMPLE:
[tex]5^{\frac{3}{4} }[/tex] = [tex]\sqrt[4]{5^3}[/tex]
Help please. 20 pts WILL MARK BRAINLIEST
Answer:
Subtract 6 from both sides
PLEASE HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Runners at a cross-country meet run 2 miles south and then 4 miles west from the starting line. Determine the shortest straight path they must run to get back to the
tarting line.
06 miles
√6 miles
O√12 miles
√20 miles
hello hope you are having a good day
the answer to your question would be A 6 miles i took the test and got an 100% also asked the teacher.
graph into an eqation
The equation of the given values of x and y will be; y = 2x - 2
What does it mean to solve an equation?An equation represents equality of two or more mathematical expression.
Solutions to an equation are those values of the variables involved in that equation for which the equation is true.
We have been given the values of x and y. then we need to find the equations;
First slope
m = (4 +2)/(3 - 0)
m = 6/3 = 2
Now the standard form of the equation is;
y-y₁ = m(x-x₁)
y+ 2 = 2(x- 0)
y = 2x - 2
The graph of the given equation of line is attached below.
Hence, the equation of the given values of x and y will be; y = 2x - 2
Learn more about solving equations here:
https://brainly.com/question/18015090
#SPJ1
What is (5,-3) & (4,0) in slope intercept form?
The slope-intercept form of (5,-3) and (4,0) is y = -3x + 12.
The slope intercept form is simply writing an equation of a line so that the slope or steepness and y-intercept i.e. where the line crosses the vertical y-axis are immediately apparent.
The slope-intercept equation is y = mx + c, where x and y are two variables, and m is slope.
Slope m = [tex]\frac{y2-y1}{x2-x1}[/tex]
Let,
(x1, y1) = (5, -3)
(x2, y2) = (4, 0)
Slope (m) = [tex]\frac{0 - (-3) }{4 - 5}[/tex]
= [tex]\frac{3}{-1}[/tex]
= -3
By substituting x, y, and m values in the equation we can get the value of c.
Consider x = 4 , y = 0, m = -3
y = mx + c => 0 = (-3)4 + c
c = 12
Therefore, the slope-intercept form of (5,-3) and (4,0) is y = -3x + 12.
To know more about slope-intercept form:
https://brainly.com/question/9682526
determine the sampling error if the grade point averages for 10 randomly selected students from a class of 125 students has a mean of
Answer:
Step-by-step explanation:
x=2.3
Which is the focus and directrix of the parabola with equation (y + 0.5)² = 4(x - 1)?
O Focus (2, -0.5); directrix x = 0
O Focus (2,-0.5); directrix y = -1.5
O Focus (0, -0.5); directrix y = -1.5
O Focus (0, -0.5); directrix x = 0
The first option Focus(2,-0.5); directrix x=0 of the parabola is the correct answer.
What is a parabola?
A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line.
The general equation of a parabola is as follows:
[tex](y-k)^2=4a(x-h)[/tex]
Now, consider the given equation.
[tex](y+0.5)^2=4(x-1)[/tex]
Now, compare with the standered equation.
a=1, k=-0.5 and h=1
Here, a is positive hence, the parbola opens right side.
Focus is given by the following coordinate:
[tex](h+a,k)=(1+1,-0.5)\\=(2,-0.5)[/tex]
Now, equation of diretrix is given by the following expression:
[tex]x=h-a\\x=1-1\\x=0[/tex]
Hence, the first option Focus(2,-0.5); directrix x=0 is the correct answer.
Learn more about parabola from the following link:
https://brainly.com/question/64712
#SPJ1
Water Glasses on a shelf are broken and must be replaced.
The replacement cost can be cut in half if you can figure out how many glasses were broken.
Here are your clues:
There were more than 24 glasses, but less than 100 glasses.
If the glasses were in rows of 6, there would be 3 left over.
If the glasses were in rows of 8, there would be 7 left over.
The total number of water glasses on the shelf may be 39, 63 or 87.
Given, that there were more than 24 glasses, but less than 100 glasses.
If the glasses were in rows of 6, there would be 3 left over.
If the glasses were in rows of 8, there would be 7 left over.
Let the number of glasses be x,
So, x = 6k1 + 3
=> (x - 3) is a multiple of 6
x = 8k2 + 7
=> (x - 7) is a multiple of 8
Now, the numbers that can satisfy the given conditions are,
39 , 63 & 87.
So, the total number of glasses may be 39, 63 or 87.
Hence, the total number of water glasses on the shelf may be 39, 63 or 87.
Learn more about LCM and HCF here https://brainly.com/question/26431349
#SPJ1
The water level in a spherical bowl has a diameter of 30 cm. If the horizontal diameter of the bowl is 10 cm below the water level, calculate the radius of the bowl and the depth of the water in the bowl.
Answer:
radius ≈ 18.03 cmdepth ≈ 28.03 cmStep-by-step explanation:
You want the radius and water depth in a spherical bowl in which the water level is 10 cm above the center of the sphere, and the circular surface has a diameter of 30 cm.
Pythagorean theoremThe geometry of the diameter of the water surface can be modeled as shown in the attachment. The radius of that surface forms one leg of a right triangle with the other leg being 10 cm. The hypotenuse of the triangle is the radius of the sphere, so we have ...
r² = 15² +10² = 325
r = √325 = 5√13 ≈ 18.03 . . . . . cm
DepthThe water depth is 10 cm more than the radius, so is ...
d = 10 +r = 10 +5√13 ≈ 28.03 . . . . . cm
The radius of the bowl is about 18.03 cm; the depth of water is about 28.03 cm.
Given the Quadratic equation y = 2x²- 9x - 13, what is the y intercept?
(0,0)
(0,-13)
(0,2)
(0,-9)
Help please
Answer: (0,-13)
Step-by-step explanation:
The y intercept is x=0
Hence,
y=2(0²)-9*(0)-13
y=2(0)-0-13
y=0-13
y=-13
Thus, (0,-13)
State the coordinates of the point.
a researcher want to determine an interval estimate for the average weight of adult gorillas in pounds. she wants to be 80% certain that she is within 7.1 of the true average. from past studies, it is known that the standard deviation of the weights of adult gorillas is 18.2 pounds.
The population estimated minimum sample size will be 11 , and the critical value will be 1.28.
The average gorilla weight is being calculated as a range estimate by a researcher (in pounds).
She wants to be within 7.1 pounds of the actual average with 80% accuracy.
Previous research has shown that the standard deviation of the weights of gorillas is 18.2 pounds.
a) Since the confidence is 0.80 or 80% then the value of α is 0.20 and and we can calculate the critical value. Then the value of the z-score will be z = 1.28.
b) The margin of error is given as
M.E.= z*(standard deviation/√n)
We have,
Margin of error = 7.1
From the above formula we get;
n = ((z* standard deviation )/marginal error)²
n = ((1.28*18.2)/7.1)²
= 10.76 ≈ 11
Therefore, the researcher should take 11 samples.
To learn more about normal distribution visit;
https://brainly.com/question/12421652
#SPJ4
5. What is the independent variable in the following function?
f(c) = 2c + 9
09
Of
0:
Answer:
C
Step-by-step explanation:
C is the input. The input is the independent variable. The output would be the dependent variable.
Devon and Albert are shelving books at a public library. Devon shelves 6 books at a time, whereas Albert shelves 9 at a time. If they end up shelving the same number of books, what is the smallest number of books each could have shelved?
Factorize 6pq-3rs-3ps+6qr
with solutions
3 (2q - s)(p + r) is the factor form of expression 6pq-3rs-3ps+6qr.
What is Factor?A factor is a number that divides another number, leaving no remainder
The given expression is 6pq-3rs-3ps+6qr
We need to factorize the expression.
6pq-3rs-3ps+6qr
= 3 (2pq - rs - ps + 2qr)
= 3 (2pq + 2qr -ps - rs)
= 3 (2q(p + r) -s(p + r))
= 3 (2q - s)(p + r)
Hence, 3 (2q - s)(p + r) is the factor form of expression 6pq-3rs-3ps+6qr.
To learn more on Factors click:
https://brainly.com/question/14452738
#SPJ1
Please help
me answer both of them ASAP!! and submit it like this. Example: 1=b and 2=d
8. -a+b-7
9. m=(y-b)/x
Answer:
first one: C
second one: A
Step-by-step explanation:
4a - 5 + 3b - 2 - 2b - 5a
combine a terms:
-a - 5 + 3b - 2 - 2b
combine b terms:
-a - 5 + b - 2
combine numbers:
-a + b - 7 (this is option c)
_____________________
y = mx + b, solve for m
subtract b from both sides:
y - b = mx + b - b
y - b = mx
divide both sides by x:
(y - b)/x = mx/x
m = (y - b)/x (this is option a)
Which of the expressions below has a 7 in the
tenths place of the sum? Select all that apply.
A) 12.35 + 19.38
B) 9.89 + 4.9
C) 8.135 + 2. 644
D) 3.445 +2.382
Pls tell me!
The vector 〈4,1〉 describes the translation of A(-1, w) to A'(2x+1,\ 4) and B(8y-1,1) onto B'(3,3z) . Find the values of w, x, y, and z .
The values of the variables associated ot translation operations are (w, x, y, z) = (3, 1, 0, 2 / 3).
How to determine the values of the variables associated to translation operations
Herein we find two translation cases of points set on Cartesian plane. Translations are rigid operations of the form:
P'(x, y) = P(x, y) + T(x, y)
Where:
P(x, y) - Original pointP'(x, y) - Resulting pointT(x, y) - Translation vectorNow we proceed to determine the values of the variables w, x, y, z behind each translation operation, substitute on each component and solve the resulting formula:
T(x, y) = A'(x, y) - A(x, y)
(2 · x + 1, 4) - (- 1, w) = (4, 1)
(2 · x + 2, 4 - w) = (4, 1)
(x, w) = (1, 3)
T(x, y) = B'(x, y) - B(x, y)
(3, 3 · z) - (8 · y - 1, 1) = (4, 1)
(4 - 8 · y, 3 · z - 1) = (4, 1)
(y, z) = (0, 2 / 3)
To learn more on translations: https://brainly.com/question/12463306
#SPJ1
Can anyone possibly help me?
Function F was transformed by using f(bx) as shown below. Find the value of b
The graph of the transformation of f(x) to f(b·x), where f(1) in f(b·x) is equal to f(5) in f(x) indicates that the value of b is 5
What is the transformation of a function?The transformation of a function is represented by a function that changes one function into another function, such that the size, or position of the graph of the original function is modified
The given transformation of the function f is f(b·x)
A formula for the transformation of a function y = f(x) is the function;
y = a·f(b(x + c)) + d
Where;
The a indicates a vertical translation of the function
b indicates an horizontal dilation of f
c stands for a horizontal translation
d stands for a vertical translation
The translation in the question is f(b·x), which is a horizontal dilation, is expressed as follows;
When b > 1, the graph of f(x) shrinks horizontally
When 0 < b < 1, the graph of f(x) is stretched
At x = 1, f(x) = 1, and f(b·x) = 5
The graph of f(x) shrinks to obtain the graph of f(b·x), such that the value obtained at f(5) in f(x) is obtained at f(1) in f(b·x)
f(5) = f(b·1)
b×1 = 5
b = 5 ÷ 1 = 5
The value of b is 5
Learn more about transformation of functions here:
https://brainly.com/question/11943912
#SPJ1
The triangle below will be reflected across the line x = 5, then translated to
the left 12 units to form an image. A reflection over which line would result
in the same image?
Reflecting over the y-axis and then translating to the right 10 units
Step-by-step explanation:
Reflection over the line x=5 gives you the transformation ...
(x, y) ⇒ (2·5 -x, y) = (-x +10, y)
This is precisely the same transformation you get by reflection over the y-axis:
(x, y) ⇒ (-x, y)
followed by translation to the right 10 units:
(-x, y) ⇒ (-x +10, y)
__
Reflection over x=5 is the same as reflection over y and translation right 10.
To learn more about Reflection visit: https://brainly.com/question/28969632
#SPJ1
Layla is shipping cans of soup and boxes of pasta to a local food pantry. Each can of soup weighs 18.6 ounces and each box of pasta weighs 16 ounces. The maximum weight of the shipping box Layla will use to ship the food is 40 pounds. If Layla plans to put 15 cans of soup in the shipping box, how many boxes of pasta can she put in the same shipping box without going over the maximum weight?
Answer:
23 boxes of pasta
jake brought a bike that cost 65 when it was new if he eventually sold it for 20% of the original cost how much he sold it for
Answer:
$13
Step-by-step explanation:
$65 x 0.20 = 13
Answer: 20% off 65 is $52.00 so it was $13 saved
Tarak wants to find the value of a so that the line that passes through (10, a) and (-2, -8) has a slope of value of 1/4.
Explain how Tarak can find the a.
[tex](\stackrel{x_1}{10}~,~\stackrel{y_1}{a})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{8}-\stackrel{y1}{a}}}{\underset{run} {\underset{x_2}{-2}-\underset{x_1}{10}}} ~~ = ~~\stackrel{\textit{\LARGE m}}{\cfrac{1}{4}} \\\\\\ \cfrac{8-a}{-12}=\cfrac{1}{4}\implies 32-4a=-12\implies 44-4a=0 \\\\\\ 44=4a\implies \cfrac{44}{4}=a\implies \boxed{11=a}[/tex]
Cost of 14 apples is Rs. 120, find the cost of 20 apples
Answer:
Rs 171.40
Step-by-step explanation:
For 1 apple we have to divide 120 by 14 which is 8.57 to 2d.p.
So 20 * 8.57 = 171.4
to 2d.p. = Rs 171.40
Pls could you give me brainliest
pls:(
ƒ (x) = 4x + 5, what is the value of f (−3) and ƒ (3)?
Answer:
f(-3) = -7f(3) = 17Step-by-step explanation:
Given functions,
→ f(x) = 4x + 5
Now the value of f(-3) will be,
→ f(x) = 4x + 5
→ f(-3) = 4(-3) + 5
→ f(-3) = -12 + 5
→ [ f(-3) = -7 ]
Then the value of f(3) will be,
→ f(x) = 4x + 5
→ f(3) = 4(3) + 5
→ f(3) = 12 + 5
→ [ f(3) = 17 ]
Hence, the answer of f(3) is 17.
Substitute [tex]x=-3[/tex] into [tex]f(x)=4x+5[/tex] :
[tex]f(-3)=4(-3)+5[/tex]
[tex]=-12+5[/tex]
[tex]=-7[/tex]
Substitute [tex]x=3[/tex] into[tex]f(x)=4x+5[/tex] :
[tex]f(3)=4(3)+5[/tex]
[tex]=12+5[/tex]
[tex]=17[/tex]
[tex]\text{Hence, } f(-3)=-7 \text{ and } f(x)=17.[/tex]
Learn more about substitution of a function here:
https://brainly.com/question/24333134
#SPJ1