[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 &\$480\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &7 \end{cases} \\\\\\ A=480\left(1+\frac{0.09}{12}\right)^{12\cdot 7}\implies A=480(1.0075)^{84}\implies A\approx 899.14[/tex]
What is the product of 2(cos(45°) + i sin(45°)) and 5(cos(30°) + i sin(30°))?
Step-by-step explanation:
short step
(-isin(π/6)+2×5cos(π/6) ei π/4)
I/2+5√3 4√-1
The product of the trigonometric expressions will be 10 (cos 75° + i sin 75°).
What is trigonometry?Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
The trigonometric expressions are given below.
2 [cos(45°) + i sin(45°)] and 5 [cos(30°) + i sin(30°)]
Then the product of the trigonometric expressions is given as,
⇒ 2 [cos(45°) + i sin(45°)] × 5 [cos(30°) + i sin(30°)]
⇒ 10 [(cos 45° × cos 30° + sin 45° × sin 30° × i²) + i (sin 45° × cos 30° + cos 45° × sin 30°)]
⇒ 10 [cos (45° + 30°) + i sin (45° + 30°)]
⇒ 10 (cos 75° + i sin 75°)
The product of the trigonometric expressions will be 10 (cos 75° + i sin 75°).
More about the trigonometry link is given below.
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If 8% of the pupils in a class are absent and there are 46 present, what is the number of pupils in this class when all are present?
Answer:
50
Step-by-step explanation:
100% - 8% = 92%
Proportions:
46 ⇒ 92%
A ⇒ 100%
A = 46*100/92
A = 4600/92
A = 50
[1/3] to the power of 4 as a fraction
Answer:
[tex]\frac{1}{81}[/tex]
Step-by-step explanation:
[tex](\frac{1}{3} )^{4}[/tex]
We know this is written as
[tex]\frac{1}{3}*\frac{1}{3}*\frac{1}{3}*\frac{1}{3}[/tex]
Let's solve:
[tex]\frac{1}{3} * \frac{1}{3} = \frac{1}{9}\\ \frac{1}{9} *\frac{1}{3} = \frac{1}{27} \\\frac{1}{27} * \frac{1}{3} = \frac{1}{81}[/tex]
Mayra has 3 cats. Luis has twice as many cats as Mayra.
Write an expression for the number of cats Luis has:
Write an expression for the number of cats Luis and Mayra have together:
2. Each cat eats about ½ cup of cat food a day.
Write an expression for the amount of cat food all the cats eat in one day:
Write an expression for the amount of cat food all the cats eat in one week:
Solve.
45 = 4(a + 3) – 3
Answer:
a = 9
Step-by-step explanation:
45 = 4(a + 3) – 3
Add 3 to both sides.
48 = 4(a + 3)
Divide both sides by 4.
12 = a + 3
Subtract 3 from both sides.
9 = a
a = 9
Answer: a = 9
Find the area of one petal of the polar curve r = 5sin 2θ
The area of one petal of the polar curve r = 5 sin 2θ would be 25π/4.
How to find the area of a region?Supposing that there is no direct formula available for deriving the area, we can derive the area of that region by dividing it into smaller pieces, whose area can be known directly.
Then summing all those pieces' area gives us the area of the main big region.
The polar curve r = 5sin 2θ
When r = 0, θ = 0, π/2 which corresponds to one loop.
We need the limits to provide r=0 or cos(5x) =0 so:
Therefore the area of the region enclosed by this curve is
[tex]A = \dfrac{1}{2} \int\limits^a_b {r^{2} } \, d\theta \\\\\\A = \dfrac{1}{2} \int\limits^{\pi /2}_0 {25sin^{2}2\theta } \, d\theta \\\\\\A = \dfrac{1}{2} \times 25\int\limits^{\pi /2}_0 {sin^{2}2\theta } \, d\theta \\\\\\A = \dfrac{1}{2} \times 25\int\limits^{\pi /2}_0 \dfrac {1-cos^{2}4\theta } {2}\, d\theta\\ \\\\A = \dfrac{25}{2}( \theta - \dfrac {sin4\theta} {2})\, d\theta |^{\pi /2}_0\\\\\\A = \dfrac{25}{2} \times \dfrac{\pi }{2} \\\\\\A = \dfrac{25\pi }{4}[/tex]
Thus, the area of one petal of the polar curve r = 5sin 2θ would be 25π/4.
Learn more about the area;
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4(6x + 87)
9(5 x 89p)
(45 - 9) x 12
Answer:
Simplify????
1. 24x + 348
2. 4005p
3. 432
Step-by-step explanation:
Step-by-step explanation:
first one- 24x + 348
second one- 4005p
third one- 432
Which of these problems would require regrouping before solving?
Select the correct answer.
647 - 283
916 - 812
824 - 503
295 - 194
Triangle RST is shown below. What is the length of ST?
R
13
5
S
a.) 12
b.) 5
c.) 18
d.) 8
Answer:
A: 12
Step-by-step explanation:
Using the pythagoreom theorem, a^2+b^2=c^2. We can plug in the lengths of 5 and 13 which is 5^2+b^2=13^2. Now we can square the numbers to get 25+b^2=169. Subtract 25 from 169 to get 144. Now find the square root of 144 which is 12.
Find 5% of 110km/h
With steps please.
Answer:
5.5 km/h
Step-by-step explanation:
→ 5% of 110
→ (5/100) × 110
→ 0.05 × 110
→ 5.5 km/h
Before his shopping spree, Jim owned 133
bracelets. Then he bought 138 more
bracelets. What is the ratio of bracelets
purchased to resulting total number of
bracelets?
Answer:
271 to 133
Step-by-step explanation:
I need help phase 15 points
A. Rectangle
B. Triangle
C hexagon
D. Square
Answer:
looks like a triangle to me
Step-by-step explanation:
Grapes are on sale for $0.97 per pound and Bart wants to purchase 4 pounds of grapes. How much will he spend?
Answer:
$3.88
Step-by-step explanation:
A school is painting its logo in the shape of a triangle in the middle of its sports field. The school wants the height of the triangle to be 8 feet. The area of the logo must be less than 24 square feet. (The school doesn't want to buy more paint.) Write an inequality that describes the possible base lengths (in feet) of the triangle.
Answer:
Possible base lengths are 1, 2, 3, 4, 5
Step-by-step explanation:
Area = base x height / 2
Let base be b
b x 8 / 2 < 24 (Area < 24)
4b < 24
b < 6
Use an identity to find the value of
Answer:
sin Ф.
Step-by-step explanation:
Cos (-270) = cos 90 = 0 and sin(-270) = sin 90 = 1.
So cos ( Ф - 270) = cos Ф cos (-270) + sin Ф sin(-270)
= cos Ф * 0 + sin Ф * 1
= sin Ф.
Find the distance between the two points in simplest radical form.
(-5, -4) and (3, – 7)
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-5}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-7})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[3 - (-5)]^2 + [-7 - (-4)]^2}\implies d=\sqrt{(3+5)^2 + (-7+4)^2} \\\\\\ d=\sqrt{8^2 + (-3)^2}\implies d=\sqrt{64+9}\implies d=\sqrt{73}[/tex]
anyone knows the answer?!
Answer:
Your answer is B) Function 1 has the smaller minimum value of -14.
Step-by-step explanation:
Method 1: Looking at the Function 1 and 2 points.
Method 2:
I have graphed functions 1 and 2 onto desmos to help determine which one has the smaller minimum.
a water park sold 13 child tickets and 87 adult tickets. what percentage of the tickets sold were child tickets?
Answer:
13%
Step-by-step explanation:
Total is 100 tickets sold as 13+87=100, 13/100 is 13%
The critical value used in a 95% confidence interval for population proportion is
Answer:
A 95% confidence interval for the mean μ of a population is computed from a random sample and found to be 9 ±3. We may conclude that A. there is a 95% probability that μ is between 6 and 12.
Step-by-step explanation:
hope it helps
Maureen made a two-layer cake for her brother's graduation party. Both layers are 1 1/2 inches tall and shaped like rectangular prisms. The bottom layer is 24 inches long and 16 inches wide, while the top layer is 20 inches long and 12 inches wide. What is the total volume of the cake? Write your answer as a whole number, proper fraction, or mixed number.
Which is the simplified form of the expression StartFraction (6 Superscript negative 4 Baseline) Superscript negative 9 Baseline Over 6 Superscript 6 Baseline EndFraction?
Step-by-step explanation:
The option "StartFraction 1 Over 3 Superscript 8" is correct
That is 138 is correct answer
Therefore [(2−2)(34)]−3×[(2−3)(32)]2=138
Step-by-step explanation:
Given expression is ((2 Superscript negative 2 Baseline) (3 Superscript 4 Baseline)) Superscript negative 3 Baseline times ((2 Superscript negative 3 Baseline)
Complete the steps to calculate the density of the steel. Calculate the volume of the prism. Recall that the area of a hexagon is One-half times the apothem times the perimeter. V = cm3 Calculate the volume of the cylinder. Round to the nearest hundredth. V = cm3 Find the volume of the composite figure. V = cm3 Calculate the density by dividing the mass by the volume. D = g/cm3.
Answer:
(A) ✔ 0.45
(B) ✔ 0.06
(C) ✔ 0.39
(D) ✔ 7.77
Step-by-step explanation:
Got it right, hope this helps!
please to god help i need help, im stopid
Answer:
A and C
Step-by-step explanation:
Because the numbers are smaller so you need to look for a bigger number than what the number you have is.
Use the table to predict the number of times you will spin 3 when you spin the spinner 100 times. Spinning a Spinner Number spun Times spun You can predict that you will spin 3 times
Step-by-step explanation:
I am not sure i understand the text you put there.
what I think is clear is to find the expected number of the appearances of the number 3 when spinning the spinner 100 times.
to do this we start by checking the given information.
and we see that the given table based on the result of in total 50 spins (7+8+9+7+11+8).
when spinning the spinner additional times, we can expect the same structure of distribution of the individual possible results as before. we just scale everything to the new size of the overall sample.
before, with 50 spins, we saw the number 3 9 times.
so, with 100 spins, which is 2×50, we expect to see the number 3 then 2×9 = 18 times.
Aaron left his house at 10 45 a.m. and arrived at Bharat's house at 1 05 p.m. (e) How long did Aaron's cycle ride take him? Give your answer in hours and minutes.
Answer:
2hours 20minutes
Step-by-step explanation:
hope this helps
Can someone help me please
Answer:
∠A≅∠X AB≅XZ
∠B≅∠Z AC≅XY
∠C≅∠Y BC≅ZY
ΔABC≅ΔZXY
Step-by-step explanation:
congruent is identical in form so if the angle has one dash than look for the identical version on the other triangle
Parallelogram calculations
#1
Area
Length×Breadth5(2.5)12.5mi²#2
Area
1/2BH1/2(16)(5)8(5)40ft²#3
Area
BH24(6)144cm²#4
Area
BH7(4)28m²Answer:
Part (b)
Formula: Area of a rectangle = width × length
Substitution: Area = 2.5 mi × 5 mi
Answer: Area = 12.5 mi²
Part (c)Formula: Area of a triangle = 1/2 × base × height
Substitution: Area = 1/2 × (12 ft + 4 ft) × 5 ft
Answer: Area = 40 ft²
Part (e)Formula: Area of a parallelogram = base × height
Substitution: Area = 24 cm × 6 cm
Answer: Area = 144 cm²
Part (f)Formula: Area of a parallelogram = base × height
Substitution: Area = 7 m × 4 m
Answer: Area = 28 m²
PLEASE HELPP LATE NIGHT HWEHWHWHWHHW
what is the question tho?
What is the slope and y-intercept of the equation 5x + y = 4?
Answer: Explanation:The slope-intercept form of a linear equation is: y=mx+bWhere m is the slope and b is the y-intercept value.We can subtract 5x from each side of the equation to put the equation in slope intercept form while keeping the equation balanced:−5x+5x+y=−5x+40+y=−5x+4y=−5x+4Therefore:The slope is: m=−5The y-intercept is: b=4 or (0,4)
Step-by-step explanation:
Answer:
Slope m=-5 Y intercept=4 (-5,4)
Step-by-step explanation:
To get the slope you will need Rise over Run. 5/1 which is slope
which will make x=0 and y=4 which is y intercept.
James left a bin outside in his garden to collect rainwater. He notices that 1/4 gallons of water fills 2/3 of the bin. Write and solve an expression to find the amount of water that will fill the entire bin. Show your work. Explain your answer in words.
(100 POINTS!!!!)
Answer:
3/8 gallons
Step-by-step explanation:
Let T be the total amount of water which can fill the bin.
The equation formed will be :
2/3 × T = 1/4 gallonsNow, multiply each side by 3 :
3 × 2/3 × T = 1/4 × 32T = 3/4Divide each side by 2 :
2T/2 = 3/4 x 1/2T = 3/8 gallonsLet the total gallons be x
1/4=2/3xMultiply 3 to complete whole bin
3/4=2/3(3)x3/4=2xx=3/8gallons