hmmm so let's see first how much is 10% of the earnings of 1470.
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{10\% of 1470}}{\left( \cfrac{10}{100} \right)1470}\implies 147[/tex]
so then
[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 &\$147\\ r=rate\to 3.5\%\to \frac{3.5}{100}\dotfill &0.035\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &25 \end{cases}[/tex]
[tex]A=147\left(1+\frac{0.035}{12}\right)^{12\cdot 25}\implies A=147\left( \frac{2407}{2400} \right)^{300}\implies \boxed{A\approx 352.19}[/tex]
i need help with this
Tina and Sam are eating from the same pizza Tina eats 1/4 of the pizza and Sam eats 1/2 of the pizza how much of the pizza did they eat together
Step-by-step explanation:
The amount of pizza Tina eat
[tex] = \frac{1}{4} \\ [/tex]
The amount of pizza Sam eat
[tex] = \frac{1}{2} \\ [/tex]
The amount of pizza they eat together
[tex] = \frac{1}{2} + \frac{1}{4} \\ [/tex]
[tex] = \frac{1}{2} \times \frac{2}{2} + \frac{1}{4} \times \frac{1}{1} \\ [/tex]
[tex] = \frac{2}{4} + \frac{1}{4} \\ [/tex]
[tex] = \frac{2 + 1}{4} \\ [/tex]
[tex] = \frac{3}{4} \\ [/tex]
A pool measuring 10 meters by 26 meters is surrounded by a path of uniform width, as shown in the figure. If the area of the pool and the path combined is 1380 square meters, what is the width of the path?
Answer:
112m
Step-by-step explanation:
A = lw
A = 10(26)
A = 260
1380 - 260 = 1120
1120 = 10(w)
1120 / 10 = 112
Since the sample size is always smaller than the size of the population, the sample mean a. must be larger than the population mean b. can be smaller, larger, or equal to the population mean c. must be equal to the population mean d. must always be smaller than the population mean
Using the mean concept, it is found that the correct option regarding the sample mean is given by:
b. can be smaller, larger, or equal to the population mean.
What is the mean?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.
No matter the population mean, the sample mean is calculated as stated above, having no restrictions about it's value, hence option b is correct.
More can be learned about the mean concept at https://brainly.com/question/24628525
#SPJ1
can someone please help me out with this logarithm equation
[tex] \green{ - - - - - - - - - - - - - - - - - - }[/tex]
•— QUESTIONLogarithmic equation : log2 + log x = 1•— ANSWERThe answer is x = 5•— SOLUTIONlog¹⁰2+ log¹⁰ x = 1x >0log¹⁰2 + log¹⁰ x = 12x = 10[tex] \times \frac{10}{2} [/tex]x = 5•— Therefore, the answer is x = 5
[tex] \green{ - - - - - - - - - - - - - - - - - - }[/tex]
Please help and Please write real equation for the answer thank you
Answer:
f(x) = (3x -12)/(x² -7x +12)
Step-by-step explanation:
The equation for a rational function can be written from the clues offered by the horizontal and vertical asymptotes, the y-intercept, and any "holes" in the function graph. Here, those clues are ...
horizontal asymptote: y = 0vertical asymptote: x = 3hole: (x, y) = (4, 3)y-intercept: (0, -1)__
The horizontal asymptote at y=0 tells you the denominator is of higher degree than the numerator. The vertical asymptote at x=3 tells you (x-3) is a factor of the denominator. The hole at x=4 tells you there is a factor of (x-4) in both numerator and denominator.
At this point, the function is tentatively ...
[tex]f(x)=a\dfrac{x-4}{(x-3)(x-4)}[/tex]
Evaluating this at the y-intercept, x=0, gives ...
f(0) = -1 = a/(0 -3) = -a/3
a = 3 . . . . . multiply by -3
Then our rational function, consistent with all of the features of the graph, is ...
[tex]f(x)=\dfrac{3(x -4)}{(x -3)(x -4)}\\\\\boxed{f(x)=\dfrac{3x-12}{x^2-7x+12}}[/tex]
x is bigger than y. The difference between x and y is 18. Find x and y.
Answer:
x can be 20
y can be 2
Step-by-step explanation:
i hope i will help you
Mrs Li's classroom is 34 feet wide and 42 feet long. Objects in classroom Mrs. Li's Desk, Fish Tank, Math Center, or Reading Center. Area of Objects (square feet) 8, 6, 100, or 120. what is the area of the classroom?
Answer:
multiply length with breadth which is 34 *42
Answer:1'428 sq ft because you multiply 34x42 witch= to 1,428
what is the mean of these number 8 40 50 85 1 5 46 65 41 13 34 67 53 71 44
Answer:
41.53
Step-by-step explanation:
add all the numbers and divide by how much there is
623 /15
41.53
hope this helps!!
Use logarithmic differentiation to find dy/dx. y = (1 + x)^1/x, x > 0
Use exp/log functions to rewrite y as
[tex]y = (1+x)^{\frac1x} \implies y = \exp\left(\ln\left(1+x)^{\frac1x}\right)\right)[/tex]
One of the properties of logarithms lets us bring down the exponent, so
[tex]y = \exp\left(\dfrac{\ln(1+x)}x\right)[/tex]
Now take the derivative of both sides with respect to x. By the chain and quotient rules,
[tex]\dfrac{dy}{dx} = \exp\left(\dfrac{\ln(1+x)}x\right) \times \dfrac{\frac x{1+x} - \ln(1+x)}{x^2}[/tex]
Simplify:
[tex]\boxed{\dfrac{dy}{dx} = \frac{x - (1+x)\ln(1+x)}{x^2(1+x)} (1+x)^{\frac1x}}[/tex]
PLEASE HELP: A random sample of 200 students are chosen from a student population of 1200 students. which sample do you think is more likely to be representative of the population
Answer:
random sampling is more accurate
PLEQSE HELP ME WITH THIS!!
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer:
AB = 13 meters
Step-by-step explanation:
AB is congruent to AC and AC is 13 meters so that's what AB would be
What is the vertex for this function?
y=2x^2−12x+16
(-2, 12)
(-2, 3)
(-12, 36)
(3, -2)
Answer:
Step-by-step explanation:
hello :
y=2x²−12x+16
y = 2(x²-6x+9-9)+16
y = 2(x-3)²-18+16
y = 2(x-3)²-2.....vertex -form when the vertex is : (3, -2)
HELP ASAP
In the diagram, m ZAFB = 78°
Which angle is supplementary to ZAFB and what is its measure?
Answer:
Angle AFE = 102(degree symbol)
Step-by-step explanation:
supplementary means two angles that add up to 180
hope this helps! :)
Answer:
The angle supplementary to ∠AFB is ∠EFA.
The reason why this is, is because a supplementary angle consists of two angles that have a sum of 180°.
Supplementary angles combine to form a straight line.
In this case, ∠EFA is the supplement of ∠AFB because, ∠EFA is the other part of the angle, AFB, that creates a full straight line(180°).
And to find the value of m∠EFA you would need to arrange an equation.
Since we know that the given angle measure of AFB is 78°, ∠EFA would have to equal a different measure so that both measures will have a sum of 180°.
We will consider the value of m∠EFA to be 'x' in our equation, so;
x + 78 = 180°
Solve for x:-
-78 -78
x = 102°, therefore m∠EFA = 102°.
Write an equation of the line in slope-intercept form.
y=
Answer:
The equation of the line in slope intercept form is y=1/3x+2
Step-by-step explanation:
Based on the diagram, which expresses all possible lengths of segment AB?
AB = 25
27 < AB < 81
AB = 85
AB < 27 or AB > 81
Answer:
B. 27<AB<81 seems like the best option. AB got to be bigger than 27.
Step-by-step explanation:
Based on the diagram, possible lengths of side AB are 27 < AB < 81.
What is Triangle?Triangle is a polygon in two dimensional geometry. It consists of three sides, three angles and three vertices.
The sum of all the angles inside the triangle is equal to 180 degrees.
We have the Triangle Inequality theorem which states that the third side of a triangle is always less than the sum of the lengths of the other two sides.
So the length of side AB is always less than AC + BC.
AB < AC + BC
AB < 27 + 54
AB < 81
Now from the diagram it is clear that AC is less than AB.
AC < AB
27 < AB
Combining these inequalities, we get 27 < AB < 81.
Hence all the possible lengths of side AB is 27 < AB < 81.
To learn more about Triangles, click on the link :
https://brainly.com/question/2773823
#SPJ2
An equilateral triangle has a perimeter of 90 inches. Find the area of the equilateral triangle, I simplest form.
Answer:
389.7 square inches
Step-by-step explanation:
equilateral triangle = each side has the same lenght
90 inches / 3 = 30 inches each side
----------------------------------------------------------
Pythagoras
30^2 = 15^2 + x^2
900 - 225 = x^2
v 675 = x
25.98 = x
x = height
----------------------------------------------------------
Area = BxH/2
B = 30 inches
H = 25.98
(30 x 25.98) /2 = 389.7 square inches
Answer:
390 in²
Step-by-step explanation:
Length of the sides of the triangle = 90/3 = 30 in
area of a triangle = (base × height)/2
height of an equilateral triangle with sides of length x [tex]=\frac{\sqrt{3} }{2}x[/tex]
Then the height of our triangle [tex]=\frac{\sqrt{3} }{2} \times30=26[/tex]
Conclusion:
area of the triangle = (30 × 26)/2 = 390 in²
Jaydon has eaten 3.6% his 45 ounce block of chocolate
fudge. How many ounces of fudge has he eaten?
Answer:
The answer is 1.62 ounce
Step-by-step explanation:
Given;Jaydon has eaten 3.6% of his 45 ounce block of chocolate fudge.To Find;How many ounces of fudge has he eaten?Now,
3.6% of his 45 ounce
45 × 3.6 ÷ 100
162 ÷ 100 = 1.62
Thus, Jaydon has eaten 1.62 ounce block of chocolate fudge.
Calculate the rise and run to and the slope of each line. someone help me
Rise: -4
Run: 3
Solution:The rise is how many units we move up or down.The run is how many units we move left or right.We move down 4 units, so the rise is -4.Then, we "run" 3 units, so the run is 3.Hope it helps.
Do comment if you have any query.
) What is the volume of the container?
10 Inches
5 inches
12 inches
>) 27 cubic
60 cubic
inches
120 cubic
inches
600 cubic
inches
inches
shine
>
Answer:
600in³
Step-by-step explanation:
the equation for volume is:
V=s*3
(s is a varible which means LengthxHeightxWidth)
step 1
V= (10")(5")(12")
then it equals your answer
up above is the answer.
Hope it help you out.
Don't forget to label.
Which angles are congruent to each other?
314 11
12
109
15
5
13
210 and 212
216 and 26
215 and 27
29 and 214
Submit
X Practice in the app
Help picture below problem 12
Answer:
124°
Step-by-step explanation:
Not the best at explaining but should be equal to 180 straight across. You have to find the missing angle. You know the right angle is 90° so you will add 34° to get 124°. 180-124 will get you 56°. Straught across you have the angle that you are trying to find which is 124° because 180-56 is 124.
Question 8(Multiple Choice Worth 1 points)
(07.04 HC)
Right triangle ABC is located at A (-1, 4), B (-1, 1), and C (-5, 1) on a coordinate plane. What is the equation of a circle A with radius AC?
O(x + 1)2 + (y - 4)2 = 9
(x + 5)2 + y - 1)2 = 25
(x + 5)2 + (y - 1)2 = 16
(x + 1)2 + (y - 4)2 = 25
Answer:
(d) (x + 1)^2 + (y - 4)^2 = 25
Step-by-step explanation:
The equation of a circle with center (h, k) and radius r is ...
(x -h)² +(y -k)² = r²
__
Circle A has its center at point A, so the left side of this equation will look like ...
(x -(-1))² +(y -4)² = r² . . . . . . using (h, k) = (-1, 4)
where r is the length of segment AC. One way to find the value of r² is to use point C for (x, y):
(-5 +1)² +(1 -4)² = r²
16 +9 = r² = 25
Then the equation of the circle is ...
(x +1)² +(y -4)² = 25
A ladder 15 feet long is leaning against a house. The base of the ladder is pulled
away from the wall at a rate of 5 ft/sec. How fast is the top of the ladder moving
down the wall when its base is 1 feet from the wall? Round your answer to two
decimal places.
Answer:
it is equal to negative 5/24 feet per second, and it's negative because the ladder, the top of the ladder, is moving down the wall, so we have a negative rate.
Step-by-step explanation:
In this problem. We have a ladder that's leaning against the wall of a building. KR ladder is 13 feet long. Okay, I'm going to go ahead and label that l for ladder. You see, we form a right triangle here. I'm gonna label the horizontal acts and the vertical. Why? We are told that the bottom of the ladder is moving away from the building at a rate off 0.5 feet per second. So that's DX DT. Secret will 0.5 feet per second. What we're trying to find is how quickly the top of the ladder is moving down the wall when the base of the ladder is five feet from the wall. Okay, so the point where X is five feet, we want to know how quickly the latter is moving down the wall. So we have a Pythagorean theorem here. X squared plus y squared is equal to elsewhere. I want to go ahead and substitute in 13 for L. Because that is constant. It's not going to change so we can go ahead and put in 13. I want to take the derivative of both sides with respect to t. I'm gonna have to X dx DT plus two. Why d y d t and that's going to be equal to will. The derivative of a constant is just zero. Now I'm gonna substitute in what? We know. I have a two here. I know. Access five. I knew. Know that DX DT is 0.5. I do not know why at this point, OK, But I know I'm trying to solve for d y t t. So I'm gonna go have put that in there. So off to the side. I have to figure out what? Why is well using my migrant there? I'm here. I know access five I'm solving for why? And I know l is 13. So why squared is going to be equal to 13 squared minus five squared, which is 144. Why is equal to 12 so I can go ahead and put 12 in here going to calculate this out? This is gonna be five plus 24 d Y d t is equal to zero. 24 d Y d t is going to be equal to negative five, so it is equal to negative 5/24 feet per second, and it's negative because the ladder, the top of the ladder, is moving down the wall, so we have a negative rate.
The top of the ladder moving down the wall when its base is 1 feet from the wall is 6.86 ft per second.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given that the base of the ladder is pulled away from the wall at a rate of 5 feet per second when its base is 1 feet from the wall. Then the time will be;
Speed = distance/time
2 = 7/t
t = 7/2 = 3.5 seconds
Using pythagorean theorem to get the length L of the wall;
L² = 25² - 7²
L = 24
The ladder will move down the length at the same time.
Rate = 24/3.5
Rate = 6.86 ft/s
Learn more about the unitary method, please visit the link given below;
https://brainly.com/question/23423168
#SPJ2
Name all the common multiples of 3 and 8 that are less than 50
find the slope of the line (3,5) (7,3)
.....................❣..........................
Please help I’m terrible at math!
Answer:
5) A - slope is positive, b = 0
6) D - slope is negative, b = 1, function is linear
7) D - b = 0
8) C - slope is negative, b = negative
Step-by-step explanation:
Hope this helps!
if x-y= -10 and x-y=2 what is the value of x
Answer:
No solutions
Step-by-step explanation:
if x-y=-10, then x<y
but in x-y=2, x>y
x cannot be bigger than and less than y at the same time
The segments shown below could form a triangle.
д
C
B
9
11
B
C
O A. True
B. False
Answer:
hi the answer is true
Step-by-step explanation:
hope it helps
The triangle can be formed using the given line segments. Therefore, the given statement is true.
What is the triangle inequality theorem?The triangle inequality theorem describes the relationship between the three sides of a triangle. According to this theorem, for any triangle, the sum of lengths of two sides is always greater than the third side.
Given that, line segments AC=9 units, BC=4 units and AB=11 units.
If a, b and c are the lengths of the sides of a triangle then
If a ≤ b ≤ c, then a + b > c.
9+4>11
13>11
Therefore, the given statement is true.
To learn more about the triangle inequality theorem visit:
https://brainly.com/question/1163433.
#SPJ7
