Answer:
P=141,300(1+0.05)^6
Step-by-step explanation:
r = rate = 5/100 = 0.05
a = starting amount = 141,300
t = time = 6 years
% growth formula:
a(1+r)^t
141,300(1.05)^6
Answer:
P=141,300(1+0.05)^6
Step-by-step explanation:
r = rate = 5/100 = 0.05
a = starting amount = 141,300
t = time = 6 years
% growth formula:
a(1+r)^t
141,300(1.05)^6
100 points!!! Please help with this math.
Answer:
12ft
Step-by-step explanation:
A prism is a 3D shape which has the same 2D shape repeated along its length (this is sometimes called the cross section).
The 2D shape at the ends of the prism is the base of the prism, so for this shape, the bases are the triangles.
The height of the prism is actually the length of the prism, so for this prism the height is 12 ft.
Tiesha made 36 cookies. There are 6 dark chocolate chips in each cookie. Some of the cookies, c, also have 4 white chocolate chips in them each. In all, the cookies have 232 chocolate chips in them. Which equation represents this situation?
A.
(36 × 6) + (c × 4) = 232
B.
(36 × 4) + c = 232
C.
c × 36 = 232
Answer:
Your answer would be:
A.) (36 × 6) + (c × 4) = 232
Step-by-step explanation:
Have a great rest of your day
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If u = 3 inches, v = 4 inches, w = 7 inches, x = 7 inches, y = 8 inches, and z = 4 inches, what is the area of the object?
Answer:270
Step-by-step explanation:
Length:
U = 3 inches
W = 7 inches
Y = 8 inches
Add them up: 18 inches all together.
Width:
V = 4 inches
X = 7 inches
Z = 4 inches
Add them up: 15
A= L x W —> 15 x 18 = 270
Koalas weigh 6 kilograms on average. how many cells are in the average koala.
Solve the question in the picture and write the correct answer
Answer:
36.24 cm²
Step-by-step explanation:
The shaded region is the inscribed circle in the isosceles triangle. In order to find its area, we need to know the radius of the circle.
__
One way to find the radius of the circle is to make use of the Angle Bisector theorem. It tells us an angle bisector divides the sides of a triangle proportionately. In the attached figure, that means angle bisector CD divides segment AE in proportion to sides CA and CE.
Side LengthTo make use of this theorem, we need to know the length of side CA. That is the hypotenuse of right triangle AEC, so can be found using the Pythagorean theorem. Isosceles triangle ABC is given as having height AE=10 and base BC = 12.
CA² = CE² +AE²
CA² = 6² +10² = 136 . . . . . . . CE is half the base length: 12/2 = 6
CA = √136 = 2√34
__
RadiusNow we can write the proportion using the angle bisector theorem.
DE/CE = DA/CA
r/6 = (10 -r)/(2√34)
r√34 = 3(10 -r) . . . . . . . multiply by 6√34
r(3 +√34) = 30
r = 30/(3 +√34)
__
AreaFrom this, we can find the area of the shaded circle to be ...
A = πr² = (3.14)(30/(3 +√34))²
= 3.14·900/(43 +6√34) ≈ 36.2374 . . . cm²
The area of the shaded region is about 36.24 cm².
_____
Additional comment
Using area considerations, the formula for the radius of the inscribed circle in an isosceles triangle with base 'b' and sides 'a' can be found to be ...
[tex]r=\dfrac{b}{2}\sqrt{\dfrac{2a-b}{2a+b}}[/tex]
For a=√136 and b=12, this becomes ...
[tex]r=\dfrac{12}{2}\sqrt{\dfrac{2\sqrt{136}-12}{2\sqrt{136}+12}}=6\sqrt{\dfrac{(\sqrt{34}-3)^2}{34-9}}=1.2(\sqrt{34}-3)\approx3.39714[/tex]
This is the same value we found above.
your dog weighs 18 kilograms. the medication dosage is 1 milliliter per every 10 pounds. rounded to the nearest milliliter, how many milliliters of medication should you give your dog? 1 kilogram = 2.2 pounds
A) 2mL
B) 3mL
C) 4mL
D) 5mL
Answer:4mL
Step-by-step explanation: if you multiply 18 by 2.2 you would get 39.6, you would divide by 10 to get 3.96, then you would round to the nearest whole number so you’d get 4.
By using a change of units, we will see that the dog needs 4 mL of medication.
How many milliliters of medication should you give your dog?
Here we need to see how many pounds are in 18 kilograms, using the relation:
1kg = 2.2lb
We get:
18 kg = 18*(2.2lb) = 39.6 lb
Now, for each 10 lb, we add 1mL of medication, then we need to divide the mass of the dog by 10lb, we get:
M = (39.6 lb)/(10 lb) = 3.96
Rounding to the next whole number we get 4, so the dog needs 4 mL of medication.
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1. Suppose that a theater charges a school group $4.50 per student to show a special film. Suppose that the theater's operating expenses include $130 for the staff and a film rental fee of $1.25 per student.
a. What equation relates the number of students x to the theater's income I?
b. What equation relates the theater's operating expenses E to the number of students x?
c. Copy and complete the table below.
Theater Income and Expenses
Number of Students, x 0 10 20 30 40 50 60 70
Income, I ($) box box box box box box box box
Expenses, E ($) box box box box box box box box
d. On the same set of axes, graph the theater's income and operating expenses for any number of students from 0 to 100.
e. Describe the patterns by which income and operating expenses increase as the number of students in a group increases.
f. Write and solve an equation that you can use to answer the question “How many students need to attend the movie so that the theater's income will equal its operating expenses?”
g. Write an equation that represents the theater's profit. Compare your equation to those your classmates wrote.
h. Find the number of students that make each of the following inequality statements true.
i. E < 255
ii. I > 675
The functions I(x) and E(x) of the theatre's income and expenses are illustrations of linear functions.
The equation of the theatre's incomeThe theatre charges $4.50 per student.
Assume the number of students is x, the equation of the theatre's income would be:
I(x) = 4.5x
The equation of the theatre's expensesThe theatre expense per student is $1.25, and the operating cost on the staff is $130
The equation of the theatre's expenses would be:
E(x) = 1.25x + 130
Complete the tableUsing the formulas I(x) = 4.5x and E(x) = 1.25x + 130, the complete table is:
Students, x 0 10 20 30 40 50 60 70
Income, I 0 45 90 135 180 225 270 315
Expenses, E 130 142.5 155 167.5 180 192.5 205 217.5
The graph of the theatre's income and expensesSee attachment
The pattern by which theatre's income and expenses increaseThe functions I(x) and E(x) are linear functions.
So, the pattern with which the functions increase is a linear pattern.
The number of students when the theatre's income and expenses are equal
This means that:
I(x) = E(x)
So, we have:
4.5x = 1.25x + 130
Subtract 1.25 from both sides
3.25x = 130
Divide both sides by 3.25
x = 40
Hence, the number of students is 40
The theatre profitThis is the difference between the theatre expenses and their income.
So, we have:
P(x) = E(x) - I(x)
This gives
P(x) = 1.25x + 130 - 4.5x
Simplify
P(x) = 130 - 3.25x
Solution to the inequalitiesWe have:
E(x) < 255
This gives
1.25x + 130 < 255
Subtract 130 from both sides and divide by 1.25
x < 100 students
Also, we have:
I(x) > 675
This gives
4.5x > 657
Solve for x
x > 146 students
Hence, the number of students for the inequalities are less than 100 and greater than 146
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Triangle ABC has an area of 25 square feet and a perimeter of 65.5 feet. △ABC is dilated by a factor of 5/2 to create △DEF. \
Calculate the area of ABC using the scale factor.
Calculate the perimeter of DEF using the scale factor.
Answer:
Solution. To find the perimeter of \triangle ABC we use the Pythagorean Theorem which tells us that |AB|^2 = |AC|^2 + |BC|^2. Since |AC| = 5 and |BC| = 12 we find that |AB| = \sqrt{169} = 13. The perimeter of \triangle ABC is then 5 + 12 + 13 = 30 units.
what is 6(x+?)= 6x + 30
??????????
Answer:
Let y = '?'
6(x + y) = 6x + 30
6x +6y = 6x + 30
6x + 6y - 6x = 6x + 30 - 6x
6y = 30
6y / 6 = 30 / 6
y = 5
Is 3√2 a rational number?
Answer:
No
Step-by-step explanation:
Because sqrt 2 is not an integer
Answer:
3root2 is not a rational number
I need help making a proof for geometry! Here is the question I really need help on this question my marking period ends soon!
There are 2 parts I have to make a proof and then I also have to find the measures of AB and AC!
Answer:
Step-by-step explanation:
The perimeter of a rectangle is 12 meters. Find the maximum area of such a rectangle. You must support your answer with calculus; an answer without support will receive no credit
Answer:
9
Step-by-step explanation:
12 divided by 4 is 3
3 multiplied by 3 is 3
The maximum area of the rectangle that has a perimeter of 12 meters would be equal to 6x - x^2.
What is the area of the rectangle?The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
Let x be the length of the rectangle and y be the width of the rectangle
The perimeter of a rectangle = 2( l + b)
12 = 2(x + y)
(x +y) = 6
y = 6- x
The area of the rectangle = length × Width
= x × y
= x ( 6- x)
= 6x - x^2
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Theresa entered a photo contest. Each entry was judged by three judges in four different categories. Each category was a percent of the overall score: Originality was 20%, technique was 35%, composition was 20%, and impact was 25%. Entries could earn up to 50 points in each category.
Theresa's scores are shown in the table.
Judge Originality Technique Composition Impact
A 40 45 30 45
B 45 45 40 40
C 35 40 35 40
This equation can be used to find her weighted score for each judge.
weighted score = (weight⋅originality)+(weight⋅technique)+(weight⋅composition)+(weight⋅impact)
What was Theresa's weighted score from each judge?
Enter your answers in the boxes.
Theresa's weighted score for Judge A was
.
Theresa's weighted score for Judge B was
.
Theresa's weighted score for Judge C was
.
Question 2
What is Theresa's overall average score from the three judges?
Enter your answer in the box. Round your answer to the nearest tenth.
points
Step-by-step explanation:
Judge A: 41 (0.20 x 40)+(0.35 x 45)+(0.20 x 30)+(0.25 x 45)
Judge B: 42.75 (0.20 x 45)+(0.35 x 45)+(0.20 x 40)+(0.25 x 40)
Judge C: 38 (0.20 x 35)+(0.35 x 40)+(0.20 x 35)+(0.25 x 40)
Total score: 40.6
The population of Bloom Falls, Mass (population 937)is slowly moving to a
bigger city. Every year the population drops by 4.5%.
What is the population after 3 years
Answer:
Step-by-step explanation:
When the population drops by 4.5%, there will be (1 - 4.5%) = 0.955 portion of the original population staying. When it happens 3 years in a row with an original population of 937, there will be:
937*0.955*0.955*0.955 = 816.11
~816 people staying in Bloom Falls.
pLs HeLp Mememememe :((((((((((((((((((((( (
Answer:
21/2
Step-by-step explanation:
10.5 is correct, but that's a decimal
21/2=10.5
Answer:
21/2
Step-by-step explanation:
10*2 = 20
then 20 + 1 = 21
to get your answer which is 21/2
PLEASE RATE!! I hope this helps!!
If you have any questions let me know
Find the angle measurements and side lengths for the triangle below
Capital letters are angels , lower case letters are sides
A=
B=
C=
a=
b=
c=
Answer:
Step-by-step explanation:
Sin(A) = 5/7
Sin(A) = 0.7143
A = sin-1(0.7143
A = 45.58
B = 180 - 45.58 - 90
B = 44.43
C = 90
c = 7
a = 5
b^2 = c^2 - a^2
b^2 = 7^2 - 5^2
b^2 = 49 - 25
b^2 = 24
b = 4.899
1. Are we limited to using a trigonometric function only in cases of an object that has a cyclical behavior? Is it possible to model physical, permanent, structures using the trigonometric functions?
2. Why can the movement of a yo-yo be modeled by a sinusoidal curve?
Trigonometric functions are not only used in cases of an object that has a cyclical behavior.
What is a trigonometric function?It should be noted that trigonometric functions are real functions that relate the angle of a right angled triangle to the ratios of the two side lengths.
Trigonometric functions are not only used in cases of an object that has a cyclical behavior. It can be used to obtain unknown angles in geometric figures.
It can also be used to model the fluctuations in temperature data for a particular year.
The movement of a yo-yo can be modeled by a sinusoidal curve since it exhibits a periodic behavior.
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Find the area of the shaded polygon.
Answer:
A = 64 sq. unStep-by-step explanation:
This is a trapezium.
The formula od an area of a trapezium:
A = 1/2(a + b) · h
We have:
a = 10, b = 6, h = 8
substitute:
A = 1/2 · (10 + 6) · 8 = 1/2 · 16 · 8 = 8 · 8 = 64
Answer:
A = 64 sq. un
Step-by-step explanation:
6 * 8 + (4 * 8)/2 =
48 + 4 * 4 =
48 + 16 =
64
What is the quotient? X^2-11x+24/(x-8)(x+2)
Answer:
D
Step-by-step explanation:
[tex]\frac{x^2-11x+24}{(x-8)(x+2)}[/tex] ← factorise the numerator
= [tex]\frac{(x-8)(x-3)}{(x-8)(x+2)}[/tex] ← cancel the common factor (x - 8) on numerator/ denominator
= [tex]\frac{x-3}{x+2}[/tex]
The quotient of the given division problem is D. (x - 3) / (x + 2).
What is Division?Division is one of the operation in mathematics where number is divided into equal parts as that of a definite number.
Given expression is,
(x² - 11x + 24) / (x - 8)(x + 2)
We have to first factor the numerator.
x² - 11x + 24 can be factored as (x - 8) (x - 3).
This is done using the factorization method.
Now the expression becomes,
(x² - 11x + 24) / (x - 8)(x + 2) = (x - 8) (x - 3) / (x - 8)(x + 2)
= (x - 3) / (x + 2)
Hence the quotient is option D.
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Identify the equation in slope-intercept form for the line containing the points
(3,5) and (2,-5)
Choices:
y = 3x − 15
y = 5x − 25
y = 10x − 25
y = 5x + 10
Pls help
Answer:
Third Option y=10x-25Step-by-step explanation:
Identify the equation in slope-intercept form for the line containing the points
(3,5) and (2,-5)
Choices:
y = 3x − 15
y = 5x − 25
y = 10x − 25
y = 5x + 10
Pls help
Sooo let’s solve this….
Notice the x-axis
Slope Intercept form changes at a constant rate soooo… from (3,5) to (2,-5)
The axis goes left by 1
On A graph the more to the left the smaller number get.
The Y-axis goes down by 10 from the bigger point
But…..
It’s really not going left 1 and 10 down you always start with the smaller point so from
(2,-5) to (3,5) It goes Right 1 and 10 up
Knowing this
Slope Intercept form
Y=mx+b
Where m=slope
b= y-intercept where the line crosses x=0
Our Slope Is 10
Because from -5 to 5 you have to add 10 to get the other value
y=10x+b
But lets just figure out the y-intercept to be sure.
We want the X-axis to be 0 so we will be going left until we get to 0
So We get this point (2,-5)
Knowing that we go up 10 and right 1 to get to the higher value we will do the opposite.
We will go 1 to the left and 10 down
(2,-5)
(1,-15)
(0,-25) As you can see x=0 so the y-intercept will be -25
y=mx+b
m=slope
b= y-intercept
y=10x-25 The Third Option is the Answer….
SonicIsCoool, at your service if you need any help :)
Which set of steps can be used to prove the sine sum identity, sin(x y) = sin(x)cos(y) cos(x)sin(y)?.
The trigonometry identity sin(x + y) = sinx cosy + cosx siny.
What is sin(x + y) identity in trigonometry?sin(x + y) is one of the identities in trigonometry for compound angles.
The angle (x + y) represents the compound angles.
sin(x + y) = sinx cosy + cosx siny
To prove
sin(x + y) = sinx cosy + cosx siny
Consider OX as a rotating line anti-clockwise. Let angle XOY = a
the making of an acute angle b the rotation in the same direction is
angleYOZ = b , angle XOZ = a + b
From triangle PTR,
∠TPR = 90 - ∠PRT , ∠ROX = a
From the right-angled triangle PQO
sin(a + b) = PQ/OP
= (PT + TQ) / OP
= PT/OP + TQ/OP
= PT/PR × PR/OP + RS/OR × OR/OP
= cos (∠TPR ) sinb + sina cosb
= sina cosb + cosa sinb
if we replace a=x and b=y
Therefore, sin(x + y) = sinx cosy + cosx siny.
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Figure #2 Volume =____ in^3
Answer:
480 in^3
Step-by-step explanation:
Multiplying the length of each of the sides together gives the volume, so [tex]12*4*10=480[/tex]
Dan the trainer has two solo workout plans that he offers his clients: Plan A and Plan B. Each client does either one or the other (not both). On Monday there were 3 clients who did Plan A and 5 who did Plan B. On Tuesday there were 6 clients who did Plan A and 2 who did Plan B. Dan trained his Monday clients for a total of 10 hours and his Tuesday clients for a total of 10 hours. How long does each of the workout plans last?
*Please help me by today if able*
What is the mode of the data set?
8
9
10
5
Answer:
8
Step-by-step explanation:
It has the highest frequency
what are the names of transversal lines?
Ty po in advance♡︎
REPORT:
NON SENSE ANSWER
NAGHAHAKOT NG PTS
BRAINLIEST:
RIGHT ANSWER
A transversal line is a line that crosses through two lines on the same plane.
Example:
I attached a photo below showing the Transversal line (the line in red) crossing two lines located on the same plane. Note: The Transversal line is only the red line, not the whole diagram below.
I am open to corrections if I unintentionally added false information :).
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Square roots are the opposite of ____________.
Answer:
Squaring a number.
Step-by-step explanation:
The square root is an operation that undoes an exponent of 2, which is the inverse operation of squaring a number.
Find the highest number which divides 144,384 and 432 without leaving remainder
Answer:
i think its 48
since 144384 divided by 48 would be 3008 and 432 divided by 48 would be 9. I believe thats the highest it can go to.
Last question please help!
Answer:
Angle BFC.
Step-by-step explanation:
Because angle BFD is a right angle because angle AFE is equal to BFD because of vertical angles
(5) to the 7 over 3 power
[tex]5^{7/3} = 42.75[/tex] (approximately)
using the formula [tex]x^{a/b}=\sqrt[b]{x^a}[/tex] we can solve the problem
so we rewrite it as [tex]\sqrt[3]{5^7}[/tex] and get ~42.75
Express in the form n : 1. Give n as a fully simplified fraction. 10 : 12
Answer:
[tex]\frac{5}{6}:1[/tex]
Step-by-step explanation:
[tex]10:12[/tex] divide both sides of this ratio by 12 to give a ratio in the form [tex]n:1[/tex]
[tex]\frac{10}{12}:1[/tex] which simplifies to [tex]\frac{5}{6}:1[/tex]