Answer:
[tex]\fbox{\begin{minipage}{13em}approximately 5397.9 dollar\end{minipage}}[/tex]
Step-by-step explanation:
Given:
Lachlan invested $4300 over 5 years at 4.6% p.a., compounded every 6 months.
Solve for:
Total value of his investment.
Step 1: Define the formula to calculate the total value of Lachlan's investment
Total value = Principal x (1 + rate/2)^(Year x 2)
(the rate is divided by 2 and the year is multiplied by 2 because this is compounded semi-annual, not compounded annual)
Step 2: Perform the calculation:
With Principal = 4300$, Rate = 4.6% =4.6/100 = 0.046, Year = 5
=> Total value = 4300 x (1 + 0.046/2)^(5 x 2) ≈ 5397.9$
Hope this helps!
:)
The Pythagorean theorem, also known as the pythagoras’ theorem, is a fundamental relation in the geometry among the three sides of a right triangle. What does Pythagoras’ theorem states about the area of the square of the hypotenuse and the area of the squares on the other two legs
Answer:
it states: a squared + b squared = c squared ( the hypotenuse)
Step-by-step explanation:
One leg of a right triangle is 21 inches longer than the other leg, and the hypotenuse is 39 inches.
Find the lengths of the legs of the triangle
Answer:
One leg - 15 inches
Second leg - 36 inches.
Step-by-step explanation:
One leg - x inches.
Second leg - (x + 21) inches.
Hypotenuse - 39 inches.
Using Pythagorean theorem
x² + (x + 21)² = 39²
x² + x² + 2*21x + 21² = 39²
2x² + 42x - 39² + 21² = 0
2x² + 42x - 1080 = 0
x² + 21x - 540 = 0
(x - 15)(x + 36) = 0
x = 15, x = - 36
We can use only positive value.
One leg - x inches = 15 inches
Second leg - (x + 21) inches = 15+21=36 inches.
Subtract the polynomials. (3x2+10x+5y)−(−5x2+2x−6y)
Answer:
[tex]=8x^2+8x+11y[/tex]
Step-by-step explanation:
[tex]\left(3x^2+10x+5y\right)-\left(-5x^2+2x-6y\right)\\\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\=3x^2+10x+5y-\left(-5x^2+2x-6y\right)\\=3x^2+10x+5y+5x^2-2x+6y\\=3x^2+5x^2+10x-2x+5y+6y\\\mathrm{Add\:similar\:elements:}\:3x^2+5x^2=8x^2\\=8x^2+10x-2x+5y+6y\\\mathrm{Add\:similar\:elements:}\:10x-2x=8x\\=8x^2+8x+5y+6y\\\mathrm{Add\:similar\:elements:}\:5y+6y=11y\\=8x^2+8x+11y\\[/tex]
What is the radius of a circle given by the equation x2 + y2 – 2x + 8y – 47= 0?
Answer:
8
Step-by-step explanation:
Leticia is cutting a board to make a ramp for her skateboard. The ramp will slope from the ground up to a height of 4 feet. The board will make an angle of 25° with the ground. How long should she cut the board for her ramp? *
1 point
9.46 feet long
4.41 feet long
8.58 feet long
10 feet long
Answer:
Correct option: first one -> 9.46 feet long
Step-by-step explanation:
To find the length of the board for her ramp, we just need to use the sine relation of its angle with the ground.
The opposite side to the angle is the height of the ramp, and the hypotenuse of the triangle formed is the length of the board. So, we have that:
sin(25°) = height / length
0.4226 = 4 / length
length = 4 / 0.4226
length = 9.4652 feet
So the length of the board should be 9.46 feet (correct option: first one)
A restaurant bill is $27.50. If the sales tax is 7.5% and a 20% tip is added, what is the total cost of the meal?
(PLEASE ANSWER ASAP)
Answer:
35.06
Step-by-step explanation:
So you have to multiply 27.50 by 0.075 to find the sales tax.
2.0625 ≈ 2.06
If the tip is off the original price, you multiply 27.50 by 0.2.
5.5
The whole meal is 27.50 + 5.50 + 2.06 = 35.06
Total cost of meal is $35.06.
What is percentage?A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
Given that,
The bill amount = $27.50
tax amount = 7.5%
tip amount = 20%
Now 7.5 % of bill amount
= 27.50x 7.5/100
= 27.50 x 0.075
=2.0625
≈ 2.06
Now 20% of bill amount is
= 27.50 x 20/100
= 27.50x0.2
= 5.5
Now,
The total cost
= 27.50 + 5.50 + 2.06
= 35.06
Hence $35.06 is the total cost.
Learn more about the percentage visit:
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Please help!!! WILL MARK BRAINLIEST ANSWER!!! A medical researcher designs a study that will investigate the effects of a
new drug on lowering patient's cholesterol level. The researcher randomly
selects participants for two groups. One group is given the new drug and the other group is given a placebo. Any person, within driving distance of the hospital, is allowed to participate and will be given a monetary compensation. Each sample consists of 5 patients. Select all weaknesses in the design.
b. more groups should have been
Answer:
C AND D
Step-by-step explanation:
A frustum is made by removing a small cone from a similar large cone. Work out the volume of the frustum, below. Give your answer in terms of pie
Answer:
Step-by-step explanation:
volume of cone=1/3 πr²h
volume of frustum=vol of larger cone-vol of smaller cone=1/3πR²H-1/3πr²h
=1/3π(R²H-r²h)
=1/3π(4.5²×9-3²×6)
=1/3π×9×3(4.5×1.5-2)
=9π(6.75-2)
=9π×4.75
=42.75π cm³
The volume of frustum of cone is [tex]42.75\pi[/tex]
What is frustum of cone?Frustum of cone is the part of cone when it is cut by a plane into two parts. The upper part of cone remains same in shape but the bottom part makes a frustum. To get this part of the right circular cone we have to slice it horizontally or parallel to the base.
Volume of frustum of cone = [tex]\frac{\pi H}{3} [ R^{2} + r^{2} + rR][/tex]
Where,
R = Radius of the bigger circular end
r = radius of the smaller circular end
H = height of frustum
According to the question
Original height of cone = 9 cm
Radius of the bigger circular end = 4.5 cm
Radius of the smaller circular end = 3 cm
Height of frustum = 3 cm
Volume of frustum of cone = [tex]\frac{\pi H}{3} [ R^{2} + r^{2} + rR][/tex]
= [tex]\frac{\pi 3}{3} [ 4.5^{2} + 3^{2} + 4.5*3][/tex]
= [tex]\pi [ 20.25 + 9 + 13.5][/tex]
= [tex]42.75\pi[/tex]
Hence, The volume of frustum of cone is [tex]42.75\pi[/tex] .
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The equation of the line of best fit is y = 10x + 40. What does the y-intercept represent?
A.
the total number of questions on the test
B.
the average number of hours the students spent studying
C.
the total number of hours the students spent studying
D.
the test score of a student who did not study
Answer: D
Step-by-step explanation:
For a student who did not study for the test you will still score 40 on the test by using you own knowledge.
A quadrilateral has vertices a(-4 -8) b (-2, 34) c(6,12 and d (10, -30). It undergoes the transformation (x,y) to (x/2,y/2).
What is it's scale factor?
What are the coordinates of the new vertices?
What is a dilatation?
(Will give Brainly)
Answer:
Step-by-step explanation:
scale factor:
1/2
the coordinates of the new vertices are
A (-4/2, -8/2)
A:(-2, -4)
B (-2/2, 34/2)
B: (-1, 17)
C (6/2, 12/2)
C:(3, 6)
D (10/2, -30/2)
D:(5, -15)
I guess the dilation is 2 times bigger?
Which of the following functions is graphed below? Please help ASAP
Answer:
its not very clear can you take a picture again?
Step-by-step explanation:
2 Points
A card game is being played and the 5 of spades, 9 of spades, and 9 of hearts
are drawn from a single deck. In order to win, the next card the player draws
from the deck must be higher than the highest card already drawn. What is
the probability that the next card the player draws is a winning card? (An ace
is considered to have a value of 1 and jacks, queens, and kings have a value
of 10.) Hint: A deck has 52 cards, 4 suits, and each suit has A, 2,3,4,5,6,7,8,
9,10,J,Q,K,
A. 25%
B. 24%
C. 32.6%
D. 8%
Answer:
C) 32.6%
Step-by-step explanation:
Given:
Total number of cards = 52
3 Cards already drawn = 5 of spades, 9 of spades, and 9 of hearts.
To win the next card drawn must be greater than the highest card already drawn.
Required:
Find the probability of winning
Here, the highest card already drawn is 9 of spades or 9 of hearts.
The cards higher than 9 of spades or 9 of hearts are four in number (10, J, Q, K). Since, we have 4 suits, the highest cards remaining are 4 * 4 = 16.
Also, a total of 49 cards are remaining since 3 cards are already drawn (52 - 3 = 49).
Therefore, the probability that the next card the player draws is a winning card: [tex]\frac{16}{49} = 0.326[/tex]
Convert to percentage:
0.326 * 100 = 32.6%
The table represents a linear function.
What is the slope of the function?
0-6
O -4
0 4
O 6
Answer:
- 6
Step-by-step explanation:
[tex]slope = \frac{8 - 2}{ - 2 - ( - 1)} = \frac{6}{ - 2 + 1} = \frac{6}{ - 1} = - 6[/tex]
£60 is divided between Richard, Stephen & Bridget so that Richard gets twice as much as Stephen, and Stephen gets three times as much as Bridget. How much does Richard get?
Answer: £18
Step-by-step explanation:
let Bridget get £x,
Stephen gets 3x, Richard gets 2(3x)
Equation is x + 3x + 6x = 60
10x = 60: x = 60/40 = 6
Bridget gets £6
Stephen gets 3x = 3 x 6 = £18
Richard gets 2(3x) = 2 x 18 = £36
Will give brainliest answer
Answer:
[tex]72.16 \: {units}^{2} [/tex]
Step-by-step explanation:
[tex]surface \: \: \: area \\ = {a}^{2} + 2a \sqrt{ \frac{ {a}^{2} }{4} + {h}^{2} } \\ = {5}^{2} + 2 \times 5 \times \sqrt{ \frac{ {5}^{2} }{4} + {4}^{2} } \\ = 72.16 \: {units}^{2} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Factor 16 x2 + 24 x + 9.
(16 x + 3)( x + 3)
(4 x + 3)(4 x - 3)
(4 x + 3) 2
Answer:
Step-by-step explanation:
(4x + 3)(4x+3) is the factor
the third one is the solution
Please help me quick!!!!!!!!!!!!!!!!!
Answer:
a. Yes, the evidence supports the hypothesis
Step-by-step explanation:
The evidence supports the hypothesis because it say that "the GREATER the HEIGHT from which you drop a ball ,the FASTER the ball will be traveling when it hits the ground because of gravity and you claimed that the ball dropped from a height of 6 feet has a higher speed than a ball dropped from a height of 3 feet. hope this help! :D
Which ordered pairs make both inequalities true? Check all that apply. (−5, 5) (0, 3) (0, −2) (1, 1) (3, −4)
Answer:
(0,-2) and (1,1)
Hope this helps :)
Answer: (0,-2) & (1,1)
Step-by-step explanation:
correct answers ✅
Q. Write the slope-intercept form of the equation of a line using the given graph.
Find the GCF of 22ab2 c2 and 40a 3 c2.
4a3b2c2
2ab2c2
4ac2
2ac2
Answer:
work is shown and pictured
The average cost of a movie ticket is $7.50. If this price increases annually by 7 percent, how much would a movie ticket cost in 9 years?
Answer: After 9 years, the ticket will be $13.79
Answer:
$13.79
Step-by-step explanation:
FV = PV(1+r/100)^9
A =7.50 (1+ [7/100]) ^9
A = $13.79 per ticket
Nicole bought 0.54 kilograms of apples and 0.87 kilograms of oranges. How much fruit did
she buy in all?
kilograms
Answer:
1.41
Step-by-step explanation:
You add 0.54 by 0.87
If Maria left a $10.16 tip on a breakfast that cost $86.89, approximately what percentage was the tip.
Answer:
11.6929451 %
Step-by-step explanation:
Take the amount of the tip over the total amount to find the percent left
10.16/86.89 =
.116929451
Multiply by 100 to put in percent form
11.6929451 %
Answer:
approx: 11.693%
Step-by-step explanation:
First divide the tip by the cost:
10.16/86.89
which =
0.11692945103
To get it to a percent we multiply by 100:
0.11692945103x100=
11.692945103
now all we need to do is add the percentage
11.692945103%
And it says approximately so that means round. A good place to round in a number as large as this is the thousandths place, so since the 9 next to the 2 is closer to 10 we make the 2 a 3 to fully complete the rounding.
= 11.693%
please mark brainliest and have a great day
Wich property is represented by the equation shown below? 6 x 3 = 3 x 6 A) Multiplicative inverse property B) Multiplicative identity property C) Associative property of multiplication D) Commutative property of multiplication
Answer:
D) Communicative Property of Multiplication
Please give brainliest -3-
4(2+a)=24 what is the answer
Given:
4(2 + a)= 24
Use Distributive Property:
8 + 4a = 24
Subtract 8 to both sides:
4a = 16
Divide 4 to both sides:
a = 4
Answer:
A = 4
Step-by-step explanation:
Assuming the question is asking what a is, then all you have to do is follow a few steps to get the right answer.
1) Use the distributive property to simplify the first part of the equation.
4(2+a) distribute the 4 to what is within the parenthesis, so multiply 4 to what is in the parenthesis. P.S: This also gets rid of the parenthesis.
(8 + 4a)
2) Now your equation looks like 8 + 4a = 24. Now, use inverse operations to isolate a. Inverse operations are basically using the opposite signs and processes to get some parts of an equation to another side.
2a. Subtract 8 from both sides of the equation:
8 + 4a - 8 = 24 - 8.
So now you have 4a = 16.
2b. Divide 4 from both sides of the equation.
4a/4 = 16/4
So now you have a = 4.
Final answer:
A = 4
Can someone help please
Answer:
9
Step-by-step explanation:
its perpendicular so you do the negative reciprical
Answer:
The correct answer is
A. 9
Step-by-step explanation:
Since the line is going up the slope will be positive... That leaves us with 2 options A/B. However the red line is much steeper and therefore has a greater slope so A is the answer.
Hope this helps!
- Quinn <3
HELP ASAP!!!! There is a clip below.
Answer:
7/4 x 3/2 x 1/2 = 1 5/16 or 21/16
Step-by-step explanation:
the sum of two rational numbers will always be
The sum of two rational numbers will always be rational
[tex]\frac{a}{b} +\frac{c}{d} =\frac{ad+bc}{bd}[/tex], therefore it will always be rational
HELP ME OUT ON THIS ONE ‘
Answer:
180 degrees rotation
Step-by-step explanation:
you take the. values of the object and multiply by -1 to obtain the values of the image
Which number produces a rational number when multiplied by 1/5 ?
Answer:
D. -2/3
Step-by-step explanation:
A rational number can be shown with a fraction and that's the only fraction in the answer choices
