Answer:
230° is equal to [tex]\displaystyle \frac{23 \pi}{18}[/tex] radians.
General Formulas and Concepts:
Trigonometry
Degrees to Radians Conversion: [tex]\displaystyle \frac{n\pi}{180}[/tex]
n is the degreesStep-by-step explanation:
Step 1: Define
Identify variables.
n = 230°
Step 2: Find Radians
Substitute in variable [Degrees of Radians Conversion]: [tex]\displaystyle \frac{230 \pi}{180}[/tex]Simplify: [tex]\displaystyle \frac{23 \pi}{18}[/tex]∴ 230° is equal to [tex]\displaystyle \frac{23 \pi}{18}[/tex] radians.
---
Topic: Pre-Calculus
Unit: Trigonometry
A sample of salary offers (in thousands of dollars) given to management majors is: 48, 51, 46, 52, 47, 48, 47, 50, 51, and 59. Using this data to obtain a 95 percent confidence interval resulted in an interval from 47.19 to 52.61. True or False: The confidence interval obtained is valid only if the distribution of the population of salary offers is normal.
Answer:
Step-by-step explanation:
number of samples, n = 10
Mean = (48 + 51 + 46 + 52 + 47 + 48 + 47 + 50 + 51 + 59)/10 = 49.9
Standard deviation = √(summation(x - mean)/n
Summation(x - mean) = (48 - 49.9)^2 + (51 - 49.9)^2 + (46 - 49.9)^2+ (52 - 49.9)^2 + (47 - 49.9)^2 + (48 - 49.9)^2 + (47 - 49.9)^2 + (50 - 49.9)^2 + (51 - 49.9)^2 + (59- 49.9)^2 = 128.9
Standard deviation = √128.9/10 = 3.59
Confidence interval is written in the form,
(Sample mean - margin of error, sample mean + margin of error)
The sample mean, x is the point estimate for the population mean.
Margin of error = z × s/√n
Where
s = sample standard deviation
From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score
In order to use the t distribution, we would determine the degree of freedom, df for the sample.
df = n - 1 = 10 - 1 = 9
Since confidence level = 95% = 0.95, α = 1 - CL = 1 – 0.95 = 0.05
α/2 = 0.05/2 = 0.025
the area to the right of z0.025 is 0.025 and the area to the left of z0.025 is 1 - 0.025 = 0.975
Looking at the t distribution table,
z = 2.262
Margin of error = 2.262 × 3.59/√10
= 2.57
the lower limit of this confidence interval is
49.9 - 2.57 = 47.33
the lower limit of this confidence interval is
49.9 + 2.57 = 52.47
So it is false
Which statement is true of a rectangle that has an area of 4x^2 +39x-10 square units and a width of (x+10) units
Answer: ( C ) The perimeter of the rectangle is (10x+18) Units
Step-by-step explanation: This is the right answer because I just checked and I did the math
Answer:
it is c i had the same problem
Step-by-step explanation:
5 boxes of candles contain a total of 60 candles. Every box holds the same number of candles in each box. How many boxes does the store have if they have 8 boxes?
Answer: 96 candles in 8 boxes
Step-by-step explanation:
There’s 12 candles in a box
Ruth Brown wants to borrow $2,600 for 90 days to pay her real 'estate tax. State Savings and Loan charges 7.25% ordinary interest while Security Bank charges 7.5% exact interest. A. What is the maturity value of each loan? B. Where should they borrow the money?
Answer:
Step-by-step explanation:
Ordinary interest rate = principal × rates × ( time / 360)
exact interest rate = principal × rates × ( time / 365)
for states saving and loan of rate 7.25 %
ordinary interest rate = $ 2600 × 0.0725 × ( 90 / 360) = $ 47.125
total amount due after 90 days = $ 2647.125
for Security Bank of 7.5%
exact interest = $2600 × 0.075 × ( 90 / 365) = $ 48.75
amount due after 90 days = $ 2600 + $ 48.75 = $ 2648.75
b) considering the amount to be paid at maturity it is better to borrow state savings and Loan although the difference is not really much.
To determine where Ruth Brown should borrow the money, we compared the maturity value of loans from State Savings and Loan and Security Bank. After computing the interest over 90 days, it is evident that State Savings and Loan offers a better deal with a lower maturity value than Security Bank, making it the preferable option.
To determine the maturity value of each loan offered to Ruth Brown, we will calculate the total amount due, including principal and interest, for both the State Savings and Loan and Security Bank, after 90 days. The interest is calculated using the formulas for ordinary interest (360-day year) and exact interest (365-day year).
State Savings and Loan:
Principal (P) = $2,600
Rate (r) = 7.25%
Time (t) = 90 days
Interest (I) = P * r*(t/360) = $2,600* 0.0725 * (90/360) = $45.125
Maturity value = Principal + Interest = $2,600 + $45.125 = $2,645.125
Security Bank:
Principal (P) = $2,600
Rate (r) = 7.5%
Time (t) = 90 days
Interest (I) = P * r *(t/365) = $2,600* 0.075 * (90/365) = $46.58
Maturity value = Principal + Interest = $2,600 + $46.58 = $2,646.58
Ruth should borrow the money from the institution that offers the lowest maturity value, which in this case would be the State Savings and Loan.
What does a daz washing powder look like in 3D net GET IT ASAP
Answer:
I dont know... Never tried it.
Answer:
47
Step-by-step explanation:
not that difficult
"A bicycle factory runs two assembly lines, A and B. 95% of line A's products pass inspection and 93% of line B's products pass inspection. 60% of the factory's bikes come off assembly line B and the rest come off line A. Find the probability that one of the factory's bikes did not pass inspection and came off assembly line Upper A."
Answer:
0.02
Step-by-step explanation:
Since 60% of the factory's bikes come off assembly line B, Therefore:
The probability that the factory's bikes come off assembly line B = 60% = 0.6
Percentage line B's products pass inspection = 93% = 0.93
Percentage line B's products that do not pass inspection = 1 - 0.93 = 0.07
The probability that the factory's bikes come off assembly line A = 1 - 0.6 = 0.4
Percentage line A's products pass inspection = 95% = 0.95
Percentage line A's products that do not pass inspection = 1 - 0.95 = 0.05
Let D represent those that passes inspection and D' represent those that do not pass inspection.
P(A ∩ D') = P(A) × P(D'/A) = 0.4 × 0.05 = 0.02
P()bikes did not pass inspection and came off assembly line A) = P(A ∩ D') = 0.02
Final answer:
The probability that a bicycle failed inspection and came from assembly line A is 2%.
Explanation:
We're tasked with finding the probability that a bike did not pass inspection and came from assembly line A. First, we calculate the probability of a bike failing inspection from each line. Since 95% of line A's products pass, there is a 5% (100%-95%) chance a bike from line A fails inspection. For line B with a 93% pass rate, there's a 7% (100%-93%) chance of failure.
Next, we consider the distribution of production between lines A and B. 60% of bikes are from line B, so 40% are from line A. We then calculate the probability of a bike being from line A and failing inspection using the multiplication rule for independent events, which is P(A) times the probability of failure on line A.
P(Fail and from A) = P(A) * P(Fail | A) = 40% * 5% = 0.40 * 0.05 = 0.02 or 2%.
Therefore, the probability that a bike did not pass inspection and came from assembly line A is 2%.
Hello, please look at the attachment and do the following :
A) Complete the ven diagram. ( what number goes in the middle and what number goes to the bottom left of the diagram out of the circle?).
B) How many students study only french
C) How many students learn spanish
Answer:
A) middle: 32
Outside: 9
B) 25
C) 47
Step-by-step explanation:
71 = 14 + 25 + intersection
Intersection = 71 - 39 = 32
Outside: 80 - 71 = 9
Only french: 25
Spanish: 14 + 32 = 46
A cyclinder has a volume of 703 cm3 and a height of 18.5 cm. What can be concluded about the cyclinder? Check all that apply.
The formula for the volume of a cyclinder can be applied to find the area of the base.
To find the area of the base, multiply volume and height.
The radius of the cyclinder is half the height.
The area of the base is 38 cm2.
To verify the solution is correct, substitute the given measures and the solution into the equation and verify the result is a true statement.
Step-by-step explanation:
Cylinder volume = 703 [tex]cm^{3}[/tex], height = 18.5 cm
(i) Volume or area of the cylinder = [tex]\pi r^{2} h[/tex]
The formula for the volume of a cyclinder can be applied to find the area of the base.
Option (i) is correct
(ii) Volume or area of the cylinder = [tex]\pi r^{2} h[/tex]
The volume should be divivded by height to get the area
Option (ii) is wrong
(iv) Area of the base = [tex]\frac{703\pi }{18}[/tex] = 38[tex]\pi cm^{2}[/tex]
Option (iv) is correct
(iii) The radius of the cyclinder is half the height.
[tex]\frac{38}{2}[/tex] = 19 cm not 18.5 cm
Option (iii) is wrong
(v)Area of the base = [tex]\frac{703\pi }{18}[/tex] = 38[tex]\pi cm^{2}[/tex]
Option (v) is correct
Answer:
1 , 4 , & 5 ... which is also a , d, & e
Step-by-step explanation:
A particle starts at point A on the positive x-axis at time t = 0 and travels along the curve from A to B to C to D, as shown above. The coordinates of the particle's position (x(t), y(t)) are differentiable functions of t, where x′(t)=dxdt=−9cos(πt6)sin(πt+1√2) and y′(t)=dydt is not explicitly given. At time t = 9, the particle reaches its final position at point D on the positive x-axis. The slope of the curve is undefined at point B. At what time t is the particle at point B?
Answer:
the particle is at point B at t = 3 s
Step-by-step explanation:
Solution:-
- The coordinates of the path that a particle follows through points A to B to C.
- The coordinates of the particle position ( x , y ) are differentiable function of t, where, the rate of change of x-coordinate is given by:
[tex]x ' (t) = -9*cos (\frac{\pi *t}{6})*sin (\frac{\pi \sqrt{t + 1} }{2})[/tex]
- The slope of the curve at point B, in mathematical terms that is called the inflection point.
- The independent variable time (t) can be determined for the particle when it is at point B. Where the x'(t) is set to zero, and the critical value defines the point B.
[tex]x ' (t) = -9*cos (\frac{\pi *t}{6})*sin (\frac{\pi \sqrt{t + 1} }{2}) = 0\\\\cos (\frac{\pi *t}{6}) = 0 , sin (\frac{\pi \sqrt{t + 1} }{2}) = 0\\\\\frac{\pi *t}{6} = \frac{\pi }{2} , \frac{\pi \sqrt{t + 1} }{2} = \pi \\\\t = 3 , t = 3[/tex]
- Hence, the particle is at point B at t = 3 s.
4. Use a proportion to find the length of the missing side in the following similar figures. (1 point)
10 cm
22 cm
x= 28 cm
x= 30.8 cm
x= 6.4 cm
X = 19 cm
Answer:
x = 19cm
Step-by-step explanation:
use pythagorean theorem:
a² - c² = b²
10² - 22² = b²
100 - 484 = b²
384 = b²
√384 = b
19cm = b or x
Answer:
30.8cm
Step-by-step explanation:
i am from connexus 8th grd pre algrabra
unit 5 lesson 3
1. 1:2
2. C. yes they are similar they have porportional side lengths and = ange measures
3. x = 4.5m
4. x = 30.8cm
5. x = 6 m
i hope this helps! = ) <3
A researcher wishes to estimate the proportion of adults who have high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within 0.04 with 99% confidence if
(a) she uses a previous estimate of 0.52?
(b) she does not use any prior estimates?
Answer:
Step-by-step explanation:
Solution:-
- The sample size = n
- The Error of estimation, E = 0.04
- The confidence level, CI = 99%
a)
What size sample should be obtained when she uses previous estimate of p = 0.52?
- We are given the sample proportion p = 0.52, the required sample size is a function of confidence value and error of estimation (E):
[tex]n = p*( 1 - p ) * (\frac{Z-critical}{E})^2[/tex]
Where,
- The critical value of the confidence level = 99% would be:
significance level ( α ) = 1 - CI = 1 - 0.99 = 0.01
Z-critical = Z_α/2 = Z_0.005 = 2.575
- The required sample size (n) can be calculated:
[tex]n = 0.52*( 1 - 0.52 ) * (\frac{2.575}{0.04})^2\\\\n = 0.2304*(51.5)^2 = 611.0784[/tex]
- Hence, the minimum required sample size (n) should be = 612 adults.
b)
- If the preliminary estimate of proportion is missing or not given, we are to assume the proportion p = 0.5.
- Similarly, repeat the calculations for sample size (n) when p = 0.5
[tex]n = 0.5*( 1 - 0.5 ) * (\frac{2.575}{0.04})^2\\\\n = 0.25*(51.5)^2 = 663.0625[/tex]
- Hence, the minimum required sample size (n) should be = 664 adults.
8x^2-x^3
Help me I need the answer
Answer:
-x^2(x-8)
Step-by-step explanation
8=8a-4(a + 8) what is the answer
Answer:
Step-by-step explanation:
8=8a-4(a+8) => 8=8a-4a-32 =>4a=40 => a=10.
If you meant 8=(8a-4)(a+8), then it is 8a^2+60a-32=8 => 8a^2+60a-40=0.
Use the quadratic formula, to get your answer.
You pick a card at random. Without putting the first card back, you pick a second card at random.
1
2
3
4
What is the probability of picking a 1 and then picking a 4?
Group of answer choices
1/16
1/4
1/12
1/2
Answer:
1/12
Step-by-step explanation:
Can someone please help
Answer:
x= 52°Step-by-step explanation:
x+90°+33°+165°+20°=360° (complete angle)
x+ 308°=360°
x= 360°-308°
x= 52°
Answer:
x=52
Step-by-step explanation:
So what you would want to do is add up all of the angle measurements given. This give you 308. Now you take this number (308) and subtract it from 360, to give you the answer of 52.
Mr. Smith has a honeybee colony on his farm. On average, 1,000 bees can gather enough nectar for 1 ounce of honey each day. If Mr. Smith wants his bees to produce 3.5 pounds of honey each week, how many bees will he need in his bee colony?
Answer:
8,000 bees
Step-by-step explanation:
Final answer:
Mr. Smith will need approximately 8,000 bees in his bee colony to produce 3.5 pounds of honey each week, based on the rate of 1,000 bees producing 1 ounce of honey per day.
Explanation:
Mr. Smith needs to calculate the number of bees required to produce 3.5 pounds of honey each week.
First, we need to convert pounds to ounces because the rate given is in ounces:
3.5 pounds = 3.5 * 16 ounces/pound = 56 ounces of honey per week.
Now, we use the given rate of honey production:
1,000 bees produce 1 ounce of honey per day.
Therefore, in one week (7 days), 1,000 bees will produce 7 ounces of honey.
To find out how many bees you need to produce 56 ounces, you divide the target ounces by the ounces produced by
1,000 bees per week:
56 ounces / 7 ounces per 1,000 bees = 8,000 bees.
So, Mr. Smith will need approximately 8,000 bees in his colony to produce 3.5 pounds of honey each week.
The daily supply of oxygen for a particular multicellular organism is provided by 625 square feet of lawn. A total of 6,250 square feet of lawn would provide the daily supplies of oxygen for how many organisms?
Can someone please help me with this problem???
Answer:
10 organisms.
Step-by-step explanation:
625 Square feet of lawn.
You would simply divide 6250 by 625 and you would get 10.
Feel free to let me know if you need more help! :)
Which of the following is not considered quantitative data?
The height of the Empire State Building.
The weight of a chicken.
The taste of vanilla ice cream.
The speed of a Tesla automobile.
Looking at the scatter plot
if 3a-2b=8 and a+3b=7 what is the value of 4a+b
Answer:
Step-by-step explanation:
If a + 3b = 7, subtract 3b from both sides of the equation
-3b = -3b then you get
a = 7-3b now plug this into the other equation: 3a-2b=8
3(7-3b) - 2b = 8
21 - 9b - 2b = 8
21 - 11b = 8 add 11 b to both sides
+ 11b +11b
21 = 8 + 11b subtract 8 from both sides
-8 -8
13 = 11b
What is 4a+b?
4(7-3b) + b =
(28 - 12b) + b =
28-11b (from above 13=11b)
28 - 13 = 15
Tom's stockbroker offers an investment that is compounded continuously at an annual interest rate of 3.7%. If Tom wants a return of $25,000, how long will Tom's investment need to be if he puts $8000 initially? Give the exact solution in symbolic form and then estimate the answer to the tenth of a year.
Answer:
It'll take 38.3 years to obtain the desired return of $25,000.
Step-by-step explanation:
In order to solve a continuosly coumponded interest question we need to apply the correct formula that is given bellow:
M = C*e^(r*t)
Where M is the final value, C is the initial value, r is the interest rate and t is the time at which the money was applied. Since he wants an return of $25,000 his final value must be the sum of the initial value with the desired return. So we have:
(25000 + 8000) = 8000*e^(0.037*t)
33000 = 8000*e^(0.037*t)
e^(0.037*t) = 33000/8000
e^(0.037*t) = 4.125
ln[e^(0.037*t)] = ln(4.125)
t = ln(4.125)/(0.037)
t = 1.4171/0.037 = 38.2991
t = 38.3 years
A circular pizza that is 16 inches in diameter is cut into 5 equal slices. What is the area of one of the slices?
Answer:
40.23
Step-by-step explanation:
Area of a circular pizza is calculated by pi radius^2
or 22/7 × (16/2)^2
Radius is diameter/2 = 16/2
= 22/7 × 8^2
= 22 × 8 × 8 ÷ 7
= 201.143 ....
A circular pizza is cut into 5 slices
so the area of 1 slice of a circular pizza is
201.143 / 5 = 40.23 inches^2
The cost of a jacket increased from $70.00 to $82.60. What is the percentage increase of the cost of the jacket?
Answer:
18%
Step-by-step explanation:
Say that the percent increase was x%. So, we can write this problem as:
70 + x% * 70 = 82.60
Remember that % means "out of 100", so x% is actually the same as x/100. We can then replace x% with x/100:
70 + (x/100) * 70 = 82.60
Both terms on the left side have 70, so we can factor that common number out:
70 * (1 + (x/100)) = 82.60
Divide both sides by 70:
1 + x/100 = 82.60/70 = 1.18
Subtract 1 from both sides:
x/100 = 0.18
Multiply by 100:
x = 18
Thus, the percent increase is 18%.
Hope this helps!
Answer:
18%
Step-by-step explanation:
Increase: 12.6
12.60/70 = 0.18
Your answer: 15.26%
You have a drawer with five pairs of white socks, three pairs of black socks, and one pair of red socks. You choose one pair of socks at random each morning, starting on Monday. You do not put the socks you choose back in the drawer. Find the probability of each event. 3. You select black socks on Monday and white socks on Tuesday.
Answer:
20.8%
Step-by-step explanation:
To find the final probability, two separate events must be done and the final propagation is the multiplication of these, like this:
First event:
Probability of black socks on Monday:
Total pair of socks: 1 + 3 + 5 = 9
Number of black socks on Monday: 3
Thus:
3/9 = 1/3
Second event:
Probability of white socks on Tuesday:
Total pair of socks: 8
Number of white socks on Tuesday: 5
Thus:
5/8
Final probability:
1/3 * 5/8 = 5/24
P = 0.208
So the probability would be 20.8%
The probability of black socks on Monday = 1/3
The probability of white socks on Tuesday = 5/8
The calculation for probability:To find the final probability, two separate events must be done and the final propagation is the multiplication of these, like this:
First event:
Probability of black socks on Monday:
Total pair of socks: 1 + 3 + 5 = 9
Number of black socks on Monday: 3
Thus:
Probability will be: 3/9 = 1/3
Second event:
Probability of white socks on Tuesday:
Total pair of socks: 8
Number of white socks on Tuesday: 5
Thus:
Probability will be: 5/8
Final probability:
1/3 * 5/8 = 5/24
P = 0.208
So, the probability would be 20.8%.
Find more information about Probability here:
brainly.com/question/24756209
As a centerpiece for her design, Hevesh build a tower 72 inches tall made of dominoes that are 2 2/5 inches tall. How many rows of dominoes stacked on top of each other tower have
Answer:
72 divided by 2 2/5 (or 2.4) = 30 in a row
Answer:
the answer is 30 in a row
Step-by-step explanation:
divide 72 by 2 2/5 and you get 30 in a row of the domino's
The slope of a line is 5 /7. What is the slope of any line that is perpendicular to that line?
Answer:
-7/5
Step-by-step explanation:
The slope of a perpendicular line is the "negative reciprocal" of the slope of the original line. so just switch the numbers and put the top number into a negative.
The slope of a line is a measure of its steepness. -7/5 is the slope of the line that is perpendicular to the line of slope 5/7.
What is slope?The slope of a line is a measure of its steepness
Two lines are perpendicular if and only if the product of their
slopes is -1.
The slope of a line is 5 /7, then slope of the line perpendicular to it.
m1*m2=-1
m1 slope of first line
m2 slope of second line
Here m1=5/7
m2=?/
m1*m2=-1
5/7*m2=-1
m2=-7/5
Therefore slope of second line is -7/5 for line perpendicular to slope of a line 5/7.
To learn more on slope click here:
https://brainly.com/question/14914699
#SPJ2
Round 2,253 to hundred
Answer:
2300
Step-by-step explanation:
Answer:
2,300
Step-by-step explanation:
When we round to the hundreds place, we make sure the numbers behind the hundreds place are zero. Then we round. Here's the general rule for rounding: If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up. In this case we round the 2 in the hundreds place up to three because it is followed by a five.
Combine like terms to create an equivalent expression.
Make sure to simplify coefficients and constants as well.
2
(
1
5
m
−
2
5
)
+
3
5
2(
5
1
m−
5
2
)+
5
3
Answer:
17982m-18301
Step-by-step explanation:
The simplified expression is [tex]\( \frac{156}{5}m - 125 \).[/tex]
To combine like terms and simplify the expression [tex]\(2(15m - 25) + \frac{3}{5} \times 2(5m - 52) + \frac{5}{3}\),[/tex] we distribute the coefficients:
[tex]\[ 2 \times 15m - 2 \times 25 + \frac{3}{5} \times 2 \times 5m - \frac{3}{5} \times 2 \times 52 + \frac{5}{3} \][/tex]
[tex]\[ = 30m - 50 + \frac{6}{5}m - \frac{6}{5} \times 52 + \frac{5}{3} \][/tex]
[tex]\[ = 30m - 50 + \frac{6}{5}m - \frac{312}{5} + \frac{5}{3} \][/tex]
Now, let's combine like terms:
[tex]\[ = (30m + \frac{6}{5}m) + (-50 - \frac{312}{5}) + \frac{5}{3} \][/tex]
[tex]\[ = (30 + \frac{6}{5})m + (-50 - \frac{312}{5}) + \frac{5}{3} \][/tex]
[tex]\[ = \frac{156}{5}m - \frac{650}{5} + \frac{25}{15} \][/tex]
[tex]\[ = \frac{156}{5}m - \frac{650}{5} + \frac{75}{15} \][/tex]
Now, let's simplify the fractions:
[tex]\[ = \frac{156}{5}m - \frac{130}{1} + \frac{5}{1} \][/tex]
[tex]\[ = \frac{156}{5}m - 130 + 5 \][/tex]
[tex]\[ = \frac{156}{5}m - 125 \][/tex]
Therefore, the simplified expression is [tex]\( \frac{156}{5}m - 125 \).[/tex]
Yuki bought a pound of confetti for $ 12 $12dollar sign, 12. What is the price, in dollars, per ounce of confetti? There are 16 1616 ounces in 1 11 pound.
We have been given that bought a pound of confetti for $12. We are asked to find price per ounce of confetti.
We know that 1 pound equals 16 ounces. To find cost of per ounce confetti, we will divide total cost by 16 as:
[tex]\text{Cost of per ounce confetti}=\frac{\$12}{16}[/tex]
[tex]\text{Cost of per ounce confetti}=\frac{\$3}{4}[/tex]
[tex]\text{Cost of per ounce confetti}=\$0.75[/tex]
Therefore, the cost of per ounce confetti is $0.75
On a coordinate plane, 3 parallelograms are shown. Parallelogram A B C D has points (3, 5), (6, 5), (4, 1), (1, 1). Parallelogram A prime B prime C prime D prime has points (3, negative 5), (6, negative 5), (4, negative 1), (1, negative 1). Parallelogram A double-prime B double-prime C double-prime D double-prime has points (negative 3, negative 4), (0, negative 4), (negative 2, 0), (negative 4, 0). Which rule describes the composition of transformations that maps pre-image ABCD to final image A"B"C"D"? Reflection across the x-axis composition translation of negative 6 units x, 1 unit y. Translation of negative 6 units x, 1 unit y composition reflection across the x-axis. 90 degree rotation about point 0 composition translation of negative 6 units x, 1 unit y. Translation of negative 6 units x, 1 unit y composition 90 degree rotation about point 0.
The correct answer is Translation of negative 6 units x, 1 unit y composition reflection across the x-axis.
Here's the step-by-step breakdown:
Parallelogram A B C D to A' B' C' D':
Reflection across the x-axis: This flips the parallelogram across the x-axis, resulting in A' B' C' D'.
Parallelogram A' B' C' D' to A" B" C" D":
Translation of negative 6 units x, 1 unit y: This shifts the parallelogram 6 units to the left and 1 unit upwards, resulting in A" B" C" D".
Therefore, the overall composition of transformations is Translation of negative 6 units x, 1 unit y composition reflection across the x-axis.
castel invests $7178 in a savings account with monthly compounding. after 7 years, the balance reaches $12,543.00. What is the interest rate of the account?
Answer:
r = 129.1 %
Step-by-step explanation:
Using the compounding formula:
A = P (1 + r/t)^nt
$12, 543 = $7178 (1 + r/12)^12(7)
-7178
$5365 = (1 + r/12)^84
[tex]\sqrt[84]{5365}[/tex] = [tex]\sqrt[84]{(1 +\frac{r}{12})^{84}}[/tex]
1.107642572 = 1 + r/12
(0.108 = r/12) (12)
r = 1.2917 = 129.1 %