To solve the savings plan balance, we have to calculate the interest for 19 months. The formula for calculating interest for compound interest is given below:$$A = P \left(1 + \frac{r}{n} \right)^{nt}$$where A is the amount, P is the principal, r is the rate of interest, t is the time period and n is the number of times interest compounded in a year.
The given interest rate is 11% per annum, which will be converted into monthly rate and then used in the above formula. Therefore, the monthly rate is $r = \frac{11\%}{12} = 0.0091667$.
The monthly payment is $PMT = $250. We need to find out the amount after 19 months. Therefore, we will use the formula of annuity.
$$A = PMT \frac{(1+r)^t - 1}{r}$$where t is the number of months of the plan and PMT is the monthly payment. Putting all the values in the above equation, we get:
$$A = 250 \times \frac{(1 + 0.0091667)^{19} - 1}{0.0091667}$$$$\Rightarrow
A = 250 \times \frac{1.0091667^{19} - 1}{0.0091667}$$$$\Rightarrow
A =250 \times 14.398$$$$\Rightarrow A = 3599.99$$
Therefore, the savings plan balance after 19 months with an APR of 11% and monthly payments of $250 is $3599.99 (approx).
For such more question on months
https://brainly.com/question/5010192
#SPJ8
A group of students at a high school took a standardized test. The number of students who passed or failed the exam is broken down by gender in the following table.
Determine whether gender and passing the test are independent by filling out the blanks in the sentence below, rounding all probabilities to the nearest thousandth.
Answer:
Gender and passing the test appear to be ________, as the probability of each event occurring does not depend on the other. Both males and females pass or fail the test with similar likelihoods. To confirm this independence, you could perform a chi-square goodness-of-fit test comparing observed frequencies to expected frequencies under the null hypothesis of independence between gender and test outcome. If the calculated p-value from the test exceeds your chosen significance level, you can conclude that there is sufficient evidence to reject the null hypothesis, indicating that gender and passing the test are dependent.
an ice cream stand has 9 flavors. a group of children each buy a double scoop with 2 flavors. if none chose the same combination, how many kids are there????
Since each child buys a double scoop with 2 flavors and no two children choose the same combination, we can determine the number of children by finding the number of unique flavor combinations possible.
To calculate the number of unique flavor combinations, we can use the concept of combinations without repetition. The formula for this is given by nCr = n! / ((n-r)! * r!), where n is the total number of flavors and r is the number of flavors chosen for each double scoop.
In this case, there are 9 flavors available and each child chooses 2 flavors. Using the formula, we have:
9C2 = 9! / ((9-2)! * 2!) = 9! / (7! * 2!) = (9 * 8) / 2 = 36 / 2 = 18.
Therefore, there are 18 children in the group, as each child can choose from 18 unique flavor combinations without repetition.
For such more question on repetition
https://brainly.com/question/9134427
#SPJ8
Help Seve & Ext
Lusk Corporation produces and sells 15,100 units of Product X each month. The selling price of Product X is $21 per unit, and variable expenses are $15 per unit. A
study has been made concerning whether Product X should be discontinued. The study shows that $72,000 of the $101000 in monthly fixed expenses charged to
Product would not be avoidable even if the product was discontinued if Product X is discontinued, the monthly financial advantage (disadvantage) for the company
Subm
If Product X is discontinued, the company would have a monthly financial advantage of $61,600.
To determine the monthly financial advantage or disadvantage for the company if Product X is discontinued, we need to calculate the total revenue and total expenses associated with Product X.
Total Revenue:
Product X sells 15,100 units per month at a price of $21 per unit. Therefore, the total revenue can be calculated as:
Total Revenue = Number of Units Sold × Price per Unit
Total Revenue = 15,100 units × $21 = $317,100
Total Variable Expenses:
The variable expenses per unit for Product X are given as $15. Therefore, the total variable expenses can be calculated as:
Total Variable Expenses = Number of Units Sold × Variable Expenses per Unit
Total Variable Expenses = 15,100 units × $15 = $226,500
Total Fixed Expenses:
Out of the $101,000 in monthly fixed expenses, $72,000 would still be incurred even if Product X is discontinued. Therefore, the avoidable fixed expenses would be:
Total Fixed Expenses - Avoidable Fixed Expenses = $101,000 - $72,000 = $29,000
Monthly Financial Advantage (Disadvantage):
To calculate the monthly financial advantage or disadvantage, we subtract the total expenses (fixed and variable) from the total revenue:
Monthly Financial Advantage (Disadvantage) = Total Revenue - Total Variable Expenses - Total Fixed Expenses
Monthly Financial Advantage (Disadvantage) = $317,100 - $226,500 - $29,000
Monthly Financial Advantage (Disadvantage) = $61,600
Therefore, if Product X is discontinued, the company would have a monthly financial advantage of $61,600.
for such more question on financial advantage
https://brainly.com/question/20381852
#SPJ8
4x-3y=18 determine the missing coordinates in ordered pair
The missing coordinate in the ordered pair (5, ?) that satisfies the equation 4x - 3y = 18 is y = 2/3. Hence, the complete ordered pair is (5, 2/3).
To determine the missing coordinate in the ordered pair (5, ?) that satisfies the equation 4x - 3y = 18, we can substitute the given x-coordinate, which is 5, into the equation and solve for y.
Let's substitute x = 5 into the equation:
4(5) - 3y = 18
20 - 3y = 18
Now, we can solve for y by isolating it on one side of the equation:
-3y = 18 - 20
-3y = -2
Divide both sides of the equation by -3 to solve for y:
y = -2 / -3
y = 2/3
Therefore, the missing coordinate in the ordered pair (5, ?) that satisfies the equation 4x - 3y = 18 is y = 2/3. Hence, the complete ordered pair is (5, 2/3).
for such more question on missing coordinate
https://brainly.com/question/24737967
#SPJ8
Question
Following equation. 4x-3y=18 Determine the missing coordinate in the ordered pair (5,?) so that it will satisfy the given equation.
Sarah wants to save $20,000 to use for a down payment on a home. She deposits some money into a 4-year certificate of deposit (CD) with an annual interest rate of 4.5% compounded monthly. How much does Sarah need to deposit in the CD to reach her goal of having $20,000 in 4 years? Round your final answer to the nearest dollar.
Hint: Use the formula PV=frac(S,sup((1+i),n)).
$12.583
$16,711
$4,785
$5,000
In the triangle what is the value of x
Answer:
26.1°
Step-by-step explanation:
You want the value of angle x° in a right triangle that has the side adjacent to x being 53 cm, and the side opposite being 26 cm.
TangentThe tangent ratio is ...
Tan = Opposite/Adjacent
ApplicationThe side opposite the angle is 26 cm; the side adjacent is 53 cm. The ratio of these is ...
tan(x) = 26/53
The arctangent function is used to find the angle when the tangent is known.
x = arctan(26/53) ≈ 26.1°
The angle x° is approximately 26.1°.
__
Additional comment
The calculator must be in degrees mode.
<95141404393>
A function and its inverse are shown on the same graph.
f(x)
x
6.
Which statement describes the relationship between the
function and its inverse?
O The slope of f¹(x) is the same as the slope of f(x).
The slope of f¹(x) is the opposite as the slope of f(x).
O The x-intercept of f¹(x) is the same as the y-intercep
of f(x).
The x-intercept of f¹(x) is the opposite as the y-
intercept of f(x).
Answer:
(c) The x-intercept of f⁻¹(x) is the same as the y-intercept of f(x).
Step-by-step explanation:
You want to know the relationship between the graphs of function f(x) and its inverse f⁻¹(x).
Inverse functionThe inverse of a function maps every y-value of the original function to its corresponding x-value. That is if you have ...
f(a) = b
then the graph of f(x) contains the ordered pair (a, b).
The inverse function will have the ordered pair (b, a). That is,
f⁻¹(b) = a
ApplicationIf an ordered pair (x-intercept) of the inverse function is ...
(P, 0)
Then there will be an ordered pair (0, P) on the graph of the original function. That point is the y-intercept, and its y-coordinate is the same as the x-coordinate of the x-intercept of the inverse function.
The x-intercept of f⁻¹(x) is the same as the y-intercept of f(x).
__
Additional comment
The graphs of the two functions are mirror images of each other across the line y=x.
<95141404393>
PLEASE HELPP!! Determine if the solutions are Rational or Irrational. ILL GIVE BRAINLIEST
We can make the decision as per rational or irrational from the solution of the equations.
A. The solution is irrational
B. The solution is rational
C. The solution is rational
D. The solution is irrational
What is a rational function?
A rational solution refers to a solution that can be expressed as a ratio of two integers, where the denominator is not zero. It is a value that satisfies an equation or inequality and can be written in the form of a fraction.
For the equation[tex]5x^2 + 4x - 14 = 0[/tex], we obtain the solution as;
-2/5 ±1/5√74
For the equation we have that[tex]4x^2 + 8x - 5 =0[/tex]. The solution would be x = 1/2 or -5/2
For the third equation we have that [tex]x^2 + x - 42 = 0[/tex] The solution is x = 6 and -7
For the fourth equation; is 3x^2 + 4x - 2= 0. The solution of the equation is -2/3 ± 1/3√10
Learn more about rational function:https://brainly.com/question/27914791
#SPJ1
NO LINKS!! URGENT HELP PLEASE!!!
Please help with #13 & 14
The type of the function is a cube function
Translate left by 1 unit and translate down by 2 unitsThe function has no minimum or maximumThe equation of the parabola is y = -1/18(x - 4)² - 1
How to determine the type of the functionFrom the question, we have the following parameters that can be used in our computation:
y = (x + 1)³ - 2
The above function has a degree of 3
This means that the type of the function is a cube function
To translate the function from the parent function, we have
Translate left by 1 unit and translate down by 2 units
Also, the function has no minimum or maximum
How to determine the equation of the parabolaHere, we have
Vertex = (4, -1)
Point (-2, -3)
A parabola is represented as
y = a(x - h)² + k
Using the vertex, we have
y = a(x - 4)² - 1
Using the point, we have
a(-2 - 4)² - 1 = -3
This gives
a(-2 - 4)² = -2
So, we have
36a = -2
Evaluate
a = -1/18
Recall that
y = a(x - 4)² - 1
So, we have
y = -1/18(x - 4)² - 1
Hence, the equation is y = -1/18(x - 4)² - 1
Read more about functions at
https://brainly.com/question/27915724
#SPJ1
Solve for x and graph the answer on a number line
2
The solution to the system of inequalities in interval notation is [-2, 1].
How to solve the system of inequalities?Based on the information provided in the image below, we have the following system of inequalities;
-12 < 3x - 6
-3 ≥ 3x - 6
By adding 6 to both sides of the equation (inequality), we have;
-12 < 3x - 6
-12 + 6 < 3x - 6 + 6
-6 < 3x
-2 < x
x > -2 (flip)
-3 ≥ 3x - 6
-3 + 6 ≥ 3x - 6 + 6
3 ≥ 3x
1 ≥ x
x ≤ 1
Therefore, the solution to the system of inequalities is given by:
-2 < x ≤ 1
In interval notation, we have [-2, 1].
Read more on inequality here: https://brainly.com/question/30665021
#SPJ1
Missing information:
The question is incomplete and the complete question is shown in the attached picture.
What is the domain of y = cos^-1 x?
[–1, 1]
[0, π]
Left-bracket negative StartFraction pi Over 2 EndFraction, StartFraction pi Over 2 EndFraction right-bracket
(–∞, ∞)
The domain cannot be (–∞, ∞) as it includes values that are not valid inputs for the inverse cosine function.
The domain of the inverse cosine function, y = cos^(-1)(x) or y = arccos(x), is the set of values for which the function is defined.
In this case, the range of the cosine function, which is the set of values that x can take, is [-1, 1]. Therefore, the domain of the inverse cosine function is the range of the cosine function.
Hence, the correct answer is [–1, 1]. This is because the inverse cosine function is only defined for values of x that fall within the range of the cosine function, which is from -1 to 1.
To clarify further, the inverse cosine function is defined as the inverse of the restricted cosine function. The restricted cosine function is defined on the interval [0, π], which means that its range is [–1, 1]. The inverse cosine function "undoes" the cosine function and maps values from [-1, 1] back to the corresponding input values in [0, π]. Therefore, the domain of the inverse cosine function is [-1, 1].
The options [0, π] and (–∞, ∞) are not correct because they do not correspond to the domain of the inverse cosine function. The range of the inverse cosine function is [0, π], and the inverse cosine function is not defined for values outside the range of the cosine function. Therefore, the domain cannot be (–∞, ∞) as it includes values that are not valid inputs for the inverse cosine function.
for more such question on function visit
https://brainly.com/question/11624077
#SPJ8
find the slope intercept equation of the line through (2,3) and (6,11)
Therefore, the slope-intercept equation of the line passing through the points (2,3) and (6,11) is y = 2x - 1.
To find the slope-intercept equation of the line passing through the points (2,3) and (6,11), we can use the formula for slope:
slope (m) = (change in y) / (change in x)
First, calculate the change in y and change in x using the given points:
change in y = 11 - 3 = 8
change in x = 6 - 2 = 4
Now, substitute the values into the slope formula:
slope (m) = 8 / 4 = 2
Next, we can use the point-slope form of the linear equation:
y - y1 = m(x - x1)
Choose one of the given points, let's use (2,3), and substitute the values into the equation:
y - 3 = 2(x - 2)
Simplifying the equation:
y - 3 = 2x - 4
Rearranging the equation to the slope-intercept form (y = mx + b):
y = 2x - 1
For such more question on substitute
https://brainly.com/question/30522132
#SPJ8
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer: (C) 1/3
Step-by-step explanation:
Look at the base lengths. For A'B'C', the length is 2. For ABC, it is 6. The ratio of the length of A'B'C' to the length of ABC is 1/3. Thus the answer is C.
What is Navems manufacturing cycle efficiency (MCE) for its elevators
The manufacturing cycle efficiency (MCE) of Navems for its elevators is 38.6%
The correct answer choice is option A.
What is Navems manufacturing cycle efficiency (MCE) for its elevators?Manufacturing cycle efficiency (MCE) = Value-added production time / Total cycle time.
Value-added production time;
Inspection time = 12 days
Process time = 5 days
Total = 17 days
Total cycle time:
Wait time = 12 days
Inspection time = 12 days
Process time = 5 days
Move time = 6 days
Queue time = 9 days
= 44 days
Hence,
Manufacturing cycle efficiency (MCE) = Value-added production time / Total cycle time × 100
= 17 days / 44 days × 100
= 38.63636363636363
Approximately,
38.6%
Read more on manufacturing cycle efficiency:
brainly.com/question/14261998
#SPJ1
(a)Derive the Lagragian interpolating polynomial of degree 1, if P₁(x₁) = a + bx₁ P₁(x) = a + bxo P₁(x) = a + bx where P₁ (x₁) = f₁, P₁ (xo) = fo.
The Lagrange interpolating polynomial of degree 1 is P₁(x) = (f₁ - fo)x + (foxo - f₁xo) / (x₁ - xo).
To derive the Lagrange interpolating polynomial of degree 1, let's consider two distinct points: (x₁, f₁) and (xo, fo). The Lagrange interpolating polynomial of degree 1 can be expressed as:
P₁(x) = L₁(x)f₁ + L₂(x)fo,
where L₁(x) and L₂(x) are the Lagrange basis polynomials defined as:
L₁(x) = (x - xo) / (x₁ - xo),
L₂(x) = (x - x₁) / (xo - x₁).
Substituting these expressions into P₁(x), we have:
P₁(x) = [(x - xo) / (x₁ - xo)]f₁ + [(x - x₁) / (xo - x₁)]fo.
Simplifying further:
P₁(x) = [f₁(x - xo) + fo(x - x₁)] / (x₁ - xo).
Expanding the numerator:
P₁(x) = [f₁x - f₁xo + fox - fox₁] / (x₁ - xo).
Finally, we can rearrange the terms to obtain the Lagrange interpolating polynomial of degree 1:
P₁(x) = (f₁ - fo)x + (foxo - f₁xo) / (x₁ - xo).
For more question on polynomial visit:
https://brainly.com/question/4142886
#SPJ8
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answer: x=15
Step-by-step explanation:
If JH is a midsegment, then J is the midpoint of LK and H is the midpoint of KM. This also means that triangles JKH and triangles LKM are similar. Since H is the midpoint of KM, assume KM = 2y (KH=y). 30/x=2/1. Thus x=15.
Answer:
x = 15
Step-by-step explanation:
The midsegment of a triangle is a line segment that connects the midpoints of two sides of a triangle.
Therefore, if JH is the midsegment of ΔKLM then JH is parallel to LM, and triangles KJH and KLM are similar: ΔKJH ~ ΔKLM.
In similar triangles, corresponding sides are always in the same ratio.
Since JH is the midsegment of ΔKLM, then KJ is half the length of KL, and KH is half the length of KM. This means that JH is half the length of LM.
Given the measure of LM is 30:
[tex]x=\overline{JH}=\dfrac{30}{2}=15[/tex]
What is the answer pleaseee
The cross-sectional area of the cylinder with a base diameter of 44cm is approximately 1520.5 cm².
What is the cross-sectional area of the cylinder?A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.
The cross-sectional area of a cylinder is expressed as;
Cross-sectional area A = πr²
From the diagram:
The dameter of the base of the base of the cylinder is 44cm.
We can determine the radius by dividing the diameter by 2:
Radius r = 44 cm / 2
Radius r = 22 cm
Now, plug the value of the radius into the formula to find the cross-sectional area:
Cross-sectional area A = πr²
Cross-sectional area A = π(22 cm)²
Cross-sectional area A = 484π cm²
Cross-sectional area = 1520.5 cm²
Therefore, the cross-sectional area is approximately 1520.5 cm².
Learn about volume of cylinder here: brainly.com/question/16788902
#SPJ1
Valerie practiced the viola for 15 minutes. Chuck practiced the cello for hour.
Floyd practiced the flute for 10 minutes longer than Chuck practiced. How long did
the three friends practice together?
The three friends practiced together for 1 hour and 25 minutes.
Valerie practiced the viola for 15 minutes, while Chuck practiced the cello for an hour. Floyd practiced the flute for 10 minutes longer than Chuck.
So, Floyd practiced the flute for 1 hour + 10 minutes.
To find the total practice time, we add the individual practice times together: 15 minutes + 1 hour + 10 minutes = 1 hour and 25 minutes.
In summary, Valerie, Chuck, and Floyd practiced their instruments for a total of 1 hour and 25 minutes.
Valerie contributed 15 minutes, Chuck practiced for 1 hour, and Floyd practiced for 1 hour and 10 minutes.
Adding these times together gives us a total practice time of 1 hour and 25 minutes.
for such more questions on minutes
https://brainly.com/question/30153116
#SPJ8
6. Aboutof Bhutan's population lives in Thimphu Dzongkhag. Chhukha Dzongkhag has about of 3 4 the population of Thimphu Dzongkhag. What fraction of Bhutan's population lives in Chhukha Dzongkhag?
About of Bhutan's population lives in Thimphu Dzongkhag. Chhukha Dzongkhag has about of 3 4 the population of Thimphu Dzongkhag. Approximately 3/7 fraction of Bhutan's population resides in Chhukha Dzongkhag.
Let's denote the population of Thimphu Dzongkhag as T and the population of Chhukha Dzongkhag as C. We are given that "about 3/4" of Thimphu Dzongkhag's population is the population of Chhukha Dzongkhag.
Mathematically, this can be represented as:
C = (3/4) * T
Now, we need to determine the fraction of Bhutan's population that lives in Chhukha Dzongkhag. To do this, we need to calculate the fraction C/(T+C).
Substituting the value of C from the equation above:
C/(T+C) = [(3/4) * T] / (T + [(3/4) * T])
Simplifying the expression:
C/(T+C) = (3/4) * T / (T + (3/4) * T)
= (3/4) * T / (4/4 * T + 3/4 * T)
= (3/4) * T / (7/4) * T
= (3/4) / (7/4)
= 3/7
Therefore, the fraction of Bhutan's population that lives in Chhukha Dzongkhag is 3/7.
This calculation is based on the given information that Chhukha Dzongkhag has about 3/4 the population of Thimphu Dzongkhag.
For more such information on: fraction
https://brainly.com/question/17220365
#SPJ8
Please awnser asap I will brainlist
Answer:
The Answer Will Be 16
Step-by-step explanation:
Beacuse , To Find Number of subsets we can use 2n Where 2 is number can't be changed but n is cardinal number so it's 16
type the whole number 16
Please awnser asap I will brainlist
Answer:
{e, 24}
Step-by-step explanation:
U = {a, b, c, d, e, f, 19, 20, 21, 22, 23, 24}
X = {a, b, c, 20, 21, 22}
Y = {b, d, f, 19, 21, 23}
X' ∩ Y' = (X U Y)'
= ({a, b, c, 20, 21, 22} U {b, d, f, 19, 21, 23})'
= ({a, b, c, d, f, 19, 20, 21, 22, 23})'
={e, 24}
Pls answer this quick
Answer/Step-by-step explanation:
A cook has 6 onions that have a total mass of 900 grams and 8 apples that have a total mass of 1 kilogram. All onions are the same size, and all apples are the same size. Which has the greater mass, an onion or an apple? Explain.
1. Underline the question you need to answer.
See above
2. What units are used in the problem?
The units used are grams and kilograms.
3. What should you do before comparing the masses?
Before comparing masses you should make sure that the apples and onions unit's are both the same.
4. How many kilograms is 900 grams?
0.9 kilograms
---
This is solved by creating a proportion:
Proportion is a mathematical comparison between two ratios (or fractions) and are equal to each other.
We know that 1 kilogram = 1000 grams
You can remember this by the fact that the prefix kilo = 1000
Your proportion would be set up as:
1 kilogram/ 1000 grams = x kilograms/ 900 grams
we can multiply 900 grams on both sides to isolate x (get x by itself)
900 grams * 1 kilogram/ 1000 grams = 900 grams * x kilograms/ 900 grams
simplified it would look like:
900 kg/1000 = x kg
x = 0.9 kg
So 0.9 kilograms is equal to 900 grams.
---
5. How many grams is 1 kilograms?
There are 1000 grams in 1 kilograms.
6. What do you need to do find the mass of 1 onion and 1 apple? Explain.
To find the mass of one onion you must divide the total mass of onions (900 grams) by 6, and you get that one onion is equal to 150 grams. To find the mass of one apple you can first convert its total mass (1 k) to grams, which equals 1000 grams. Now you can take its total mass in grams and divide it by 8. You get that one apple is equal to 125 grams.
Which has the greater mass, an onion or an apple? Explain
An onion has a greater mass than the apple because one onion has mass of 150 grams, which is greater than one apple's mass of 125 grams.
A wool suit, discounted by 20% for a clearance sale, has a price tag of $636. What was the suit’s original price?
The original price of the wool suit was $795.
Let's denote the original price of the wool suit as "P."
We know that the suit was discounted by 20%, which means the discounted price is 80% (100% - 20%) of the original price.
Given that the discounted price is $636, we can set up the following equation:
0.8P = $636
To find the original price, we need to solve for P. We can do this by dividing both sides of the equation by 0.8:
P = $636 / 0.8
P = $795
Therefore, the original price of the wool suit was $795.
for such more question on original price
https://brainly.com/question/7459025
#SPJ8
Please awnser asap I will brainlist
Answer:
True
Step-by-step explanation:
The easiest way to understand this problem is to first breakdown the notation. In words, the problem is stating 9 is NOT an element of the set containing the elements 4, 1, 8, and 7. Since 4[tex]\neq[/tex]9, 1[tex]\neq[/tex]9, 8[tex]\neq[/tex]9, and 7[tex]\neq[/tex]9 then 9 is not an element of this set and the statement is true.
Do you need a home loan of $65,000 after your down payment how much will your monthly house payment be if the bank charges 5.25% apr for a loan of 25 years simplify your answer, completely round your answer to the nearest cent
To calculate the monthly house payment for a $65,000 home loan with a 5.25% annual percentage rate (APR) over a 25-year term, we can use the formula for calculating the monthly payment on an amortizing loan. The formula is:
M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
M = Monthly payment
P = Loan principal amount
r = Monthly interest rate (APR divided by 12 and expressed as a decimal)
n = Total number of monthly payments (number of years multiplied by 12)
Let's calculate the values and substitute them into the formula:
P = $65,000
r = 5.25% / 100 / 12 = 0.004375
n = 25 * 12 = 300
Now, let's plug these values into the formula:
M = 65000 * (0.004375 * (1 + 0.004375)^300) / ((1 + 0.004375)^300 - 1)
After evaluating this expression, the monthly house payment, rounded to the nearest cent, would be approximately $406.23.
For such more question on principal amount
https://brainly.com/question/30163719
#SPJ8
help me please i would appreciate it so so much
The triangles are congruent because of S.A.A
What are congruent triangles?Congruent triangles are triangles having corresponding sides and angles to be equal. This means that for two triangles to be congruent, the corresponding angles must be equal and the corresponding sides must also be equal.
In the triangles the corresponding angles are equal.
In triangle ABC, the third angle is calculated as;
180-(90+30)
= 180-120
= 60°
I'm triangle DCE, the third angle is calculated as;
180-(90+30)
= 180-120
= 60°
Therefore the two triangles are congruent because the corresponding angles are equal.
learn more about congruent triangles from
https://brainly.com/question/2938476
#SPJ1
if f(x)= 1 over 9x -2, what is f^-1(x)?
Therefore, the inverse function f^(-1)(x) of f(x) = 1/(9x - 2) is f^(-1)(x) = (2x + 1)/(9x).
To find the inverse function of f(x) = 1/(9x - 2), denoted as f^(-1)(x), we follow these steps:
Replace f(x) with y: y = 1/(9x - 2).
Swap the variables x and y: x = 1/(9y - 2).
Solve the equation for y. Begin by multiplying both sides of the equation by (9y - 2): x(9y - 2) = 1.
Distribute the x on the left side: 9xy - 2x = 1.
Add 2x to both sides: 9xy = 1 + 2x.
Divide both sides by 9x: y = (1 + 2x)/(9x).
Simplify the expression: y = (2x + 1)/(9x).
For such more question on variables
https://brainly.com/question/28248724
#SPJ8
Two sides of a triangle have lengths 43 and 67. The angle included between these sides measures 27degrees°. To the nearest hundreth, what is the length of the third side?
The length of the third side of the triangle, to the nearest hundredth, is approximately 54.75 units.
1. We have a triangle with two known side lengths: 43 and 67 units.
2. The angle included between these sides measures 27 degrees.
3. To find the length of the third side, we can use the Law of Cosines, which states that [tex]c^2 = a^2 + b^2[/tex] - 2ab * cos(C), where c is the third side and C is the included angle.
4. Plugging in the known values, we get [tex]c^2 = 43^2 + 67^2[/tex] - 2 * 43 * 67 * cos(27).
5. Evaluating the expression on the right side, we get [tex]c^2[/tex] ≈ 1849 + 4489 - 2 * 43 * 67 * 0.891007.
6. Simplifying further, we have [tex]c^2[/tex] ≈ 6338 - 5156.898.
7. Calculating [tex]c^2[/tex], we find [tex]c^2[/tex] ≈ 1181.102.
8. Finally, taking the square root of [tex]c^2[/tex], we get c ≈ √1181.102 ≈ 34.32.
9. Rounding to the nearest hundredth, the length of the third side is approximately 34.32 units.
For more such questions on length, click on:
https://brainly.com/question/28322552
#SPJ8
Identify the missing
term(s) in the polynomial
X^3 - 95
A. Both 0x^2 and 0x
B. 0x^2
C. 0x
D. 0x4
E. There are no missing terms
The missing term in the polynomial X^3 - 95 is 0x^2.
Option A (Both 0x^2 and 0x) is the correct answer choice, as 0x represents the missing term with a degree of x (linear term) as well.
In the polynomial expression X^3 - 95, we can observe that there is a missing term with an x^2 degree.
To identify the missing term, we need to consider the standard form of a polynomial expression, which is written in descending order of exponents. In this case, the highest exponent present is x^3, followed by a constant term (-95).
To fill in the missing term, we look for the term with an x^2 degree. Since it is not present in the given expression, we can conclude that the missing term is 0x^2.
Therefore, the missing term in the polynomial X^3 - 95 is 0x^2.
Option A (Both 0x^2 and 0x) is the correct answer choice, as 0x represents the missing term with a degree of x (linear term) as well.
for such more question on polynomial
https://brainly.com/question/7297047
#SPJ8
Please awnser asap I will brainlist