The account's APY is 5.12%.
Waht is APY.Annual Percentage Yield, or APY, is the rate that may be earned on an account over the course of a year and includes compound interest.
The annual percent yield, or APY, accounts for interest compounding. Because it takes into account the interest you earn on your money, it accurately reflects the interest rate you really receive on an investment.
Consider the previous illustration, where a $100 investment generates a 5% quarterly compounded return. On the $100, you receive interest throughout the first quarter. However, in the second quarter, you also receive interest on the $100 in addition to the first quarter's interest.
The APY (Annualized Percentage Yield) formula is:
APY = [tex](1+i/N)^{N} -1[/tex]
where, i = Nominal rate = 5%, N = Number of compounding periods = 12
putting the values in the above formula, we get,
APY = (1 + 5% / 12)^12 - 1
APY = (1 + 0.4167%)^12 - 1
APY = (1 + 0.0041667)^12 - 1
APY = (1.0041667)^12 - 1
APY = 1.051161897 - 1
APY = 0.051161 or 5.12%
The APY for this account 5.12%
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Please ignore the triangles on the side
best answer gets brainliest
Answer:
103.98cm
Step-by-step explanation:
14 + 14 = 28
20 + 20 = 40
(14(3.14)) / 2+ 14 = 35.98cm
40 + 28 + 35.98 = 103.98cm
Please help with these two questions!
The inverse of the function g(x) = ∛(2x + 4) is equal to: D. g(x)⁻¹ = 1/2(x³) - 2.
The domain of the function shown in the graph is: B. [-2, 1].
What is an inverse function?In Mathematics, an inverse function can be defined as a type of function that is obtained by reversing (undoing) the operation of a given function (f(x)).
In order to determine the inverse of the given function, we would interchange input value (x) and the output value (y) as follows:
g(x) = ∛(2x + 4)
x = ∛(2y + 4)
Next, we would take the cube root of both sides of the function;
x³ = 2y + 4
2y = x³ - 4
y = (x³ - 4)/2
y = x³/2 - 2
g(x)⁻¹ = 1/2(x³) - 2
How to identify the domain any graph?In Mathematics, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right as follows;
Domain = [-2, 1].
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Easy i just want confirmation What is 3 to the power of three halves equal to?
- cube root of 9
- square root of 9
- cube root of 27
- square root of 27
The 3 to the power of three halves equal to square root of 27 sqrt(27).
What is the square root?
A square root of a number x is a number y such that y² = x; in other words, a number y whose square is x. For example, 4 and −4 are square roots of 16, because 4² = ² = 16.
A square root is a number that can be multiplied by itself to give the original number.
3 to the power of 3/2 is equal to the square root of 3 to the power of 3, which is equal to the square root of 27. The square root of 27 is approximately 3.872983346207417.
To calculate this value, you can use a calculator or you can use the following formula:
3^(3/2) = sqrt(3^3) = sqrt(27) = 3.872983346207417
Hence, the 3 to the power of three halves equal to square root of 27 sqrt(27).
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need help on this one
Answer:
19 units
Step-by-step explanation:
You have midline LM marked as 6x+1 and parallel baseline IJ marked as -6x+56 in triangle IJK. You want to know the length of LM.
MidlineThe midline of a triangle is half the length of the parallel base:
LM = 1/2(IJ)
6x +1 = 1/2(-6x +56) . . . . . substitute expressions
6x +1 = -3x +28 . . . . . . . simplify
9x = 27 . . . . . . . . . . . . sdd 3x-1
x = 3
Now, we can find LM:
6x +1 = 6(3) +1 = 19
The measure of LM is 19 units.
Luis solves the following system of equations by elimination. {5s+3t=30 2s+3t=-3
The Elimination equations: 3s = 33, s = 11.
What is Equation?A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance.
Equations come in a variety of forms, including linear, quadratic, cubic, etc
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation.
To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. The statement is not an equation if there is no "equal to" symbol in it.
According to our question-
5s+3t=30
-1(2s+3t=-3)
which will eventually
5s+3t=30
-2s-3t=3
which then becomes
3s = 33, s=11
Hence, The Elimination equations: 3s = 33, s = 11.
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Molly works at an electronics store. Her last customer purchased a DVD player for $63.48 and five DVDs for $52.02, including taxes. If the customer paid her with two $100 bills, how much change should she give him?
Answer:
$84.50
Step-by-step explanation:
Add the amounts:
$63.48 + $52.02 = $115.50
Two $100 bills add to $200.
To find the change, subtract the total cost from the amount of money handed over.
$200 - $115.50 = $84.50
Molly should give him $84.50. Thus option B is the correct answer.
The change given must be equal to the balance left after deducting the price of the goods from the total money received.
In this case,
Price of goods = Price of DVD player + Price of five DVDs
= $63.48 + $52.02
=$115.50
Total Money Received = 2 x $100 = $200
Therefore, Change = Total Money Received - Price of goods
= $200 - $115.50
= $84.50
elimination method. please help
3x+4y=21
3x-2y=11
Answer:
(x, y) = (4 7/9, 1 2/3)
Step-by-step explanation:
You want to solve this system of equations using the elimination method.
3x +4y = 213x -2y = 11AnalysisFirst of all, take a look at the coefficients of the variables:
x: 3 and 3. Subtracting one from the other will eliminate x
y: 4 and -2. Adding twice the second to the first will eliminate y.
ExecutionThe easiest elimination is accomplished by subtracting the second equation from the first:
(3x +4y) -(3x -2y) = (21) -(11)
6y = 10 . . . . . . . . . . simplify
y = 10/6 = 5/3 = 1 2/3 . . . . divide by the coefficient of y
Finding xSubstitute for y to find x.
3x +4(5/3) = 21
x +20/9 = 7 . . . . . . divide by 3
x = 7 -(2 2/9) = 4 7/9
The solution is (x, y) = (4 7/9, 1 2/3).
__
Additional comment
A graphing calculator confirms this solution.
Because m < n m = n am < bn am = bn this is where the function is undefined
Answer: This is where the answer is undefined
Step-by-step explanation:
Edge 2022 :)
Answer: 5th option
Step-by-step explanation:
edge 2023
Solve the following problems
The values of x and y for fig. 1) is 5/4 and 4/7, for fig. 2) x = 15, y = 4 and for fig. 3) x = 3 and y = 2
What is Thales theorem?Thales's Theorem or Basic Proportionality Theorem states that if a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points, then the other two sides are divided in the same ratio.
Given are three figures of triangles,
Figure 1)
5/x+5 = 8/10
50 = 40+8x
x = 5/4
y = 7/7+y = 8/10
70 = 56 +8y
y = 4/7
Figure 2)
12/12+y = 18/18+6
12/12+y = 18/24
48 = 36 +3y
y = 4
12/4 = x/5
x = 15
Figure 3)
y/4 = 1.5/3
y = 2
x/6 = 1.5/3
x = 3
Hence, the values of x and y for fig. 1) is 5/4 and 4/7, for fig. 2) x = 15, y = 4 and for fig. 3) x = 3 and y = 2
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An airplane travels 100 miles in 0.4 hour. Which speeds represents the rate of the airplane?
The speed represents the rate of the plane is 250 miles/ hour.
What is speed?
The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.
An object is considered to be moving at constant speed when it travels an equal distance in an equal amount of time.
When an object travels a different distance at equal intervals of time, it is said to be moving at variable speed.
Average speed is the constant speed determined by the ratio of the total distance travelled by an object to the total amount of time it took to travel that distance.
Immediately speed is When an object is travelling at a variable pace, its speed at every given moment
Speed =distance/ time taken
= 100/0.4
= 250 miles/ hour
Hence, the speed represents the rate of the plane is 250 miles/ hour.
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Hello please solve this with steps
List the possible rational zeros of
f(x)= x^3-6x^2+6x-18 using the rational zero theorem
Answer:
±{1, 2, 3, 6, 9, 18}
Step-by-step explanation:
You want the possible rational zeros of f(x)= x^3-6x^2+6x-18.
Rational root theoremThe rational root theorem tells you the possible rational zeros are of the form ...
±{divisors of the constant term} / {divisors of the leading coefficient}
Here, the leading coefficient is 1, so its only divisor is 1.
The constant term is 18, and its divisors are 1, 2, 3, 6, 9, 18.
The possible rational roots are ±{1, 2, 3, 6, 9, 18}.
__
Additional comment
A graph shows the only real root is between 5 and 6, so none of the roots are rational.
what does x equal? ???
Answer: 6.1
Step-by-step explanation:
The sine rule states that the length of one side of a triangle divided by the sine of the angle opposing the side will be equal to the length of the other side divided by the sine of its opposing angle and the same for the last side.
This means [tex]\frac{14}{sin (90)}[/tex] = [tex]\frac{x}{sin(180-90-64)}[/tex]
14 = [tex]\frac{x}{sin(26)}[/tex]
x = 14sin(26) ≈ 6.1
if the histogram of monica's tips does not follow the normal curve, is the confidence interval still valid?
Yes , the confidence interval still valid because the sample size is large ( n = 100 is greater than 30 ).
Given :
Monica delivers pizza. She takes a simple random sample of 100 of her deliveries from the first 11 months of 2020 and finds that her tips average $3.66 with an SD of $2.19.The 90% confidence interval for Monica’s average tip size for these months has the form A + - B * C .
if the histogram of monica's tips does not follow the normal curve, is the confidence interval still valid .
Here
sample size n = 100
The sample size is a term used in market research for defining the number of subjects included in a sample size.
here
n > 30
Hence the confidence interval is still valid .
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Full question:
Monica delivers pizza. She takes a simple random sample of 100 of her deliveries from the first 11 months of 2020 and finds that her tips average $3.66 with an SD of $2.19.The 90% confidence interval for Monica’s average tip size for these months has the form A + - B * C .
if the histogram of monica's tips does not follow the normal curve, is the confidence interval still valid?
A construction worker must raise to the top of a 20-foot-tall building using a computer-controlled crane. If the materials are 28 feet away from the base of the building. What slope needs to be programmed into the computer to accomplish the delivery? State your answer as a fraction in lowest terms
The slope that needs to be programmed into the computer to accomplish the delivery is x=3441/100.
What is meant by Pythagorean theorem?A fundamental relationship in Euclidean geometry between a right triangle's three sides is known as the Pythagorean theorem or Pythagoras theorem in mathematics. It is believed that the area of the square with the hypotenuse equals the sum of the areas of the squares on the other two sides.
Pythagoras, a Greek philosopher who was born around 570 BC, is honored in the name of the theorem. Perhaps more than any other mathematical theorem, the theorem has been demonstrated several times using a variety of techniques. There are many different types of proofs, some of which go back thousands of years, including both geometric proofs and algebraic proofs.
By using Pythagorean theorem,
x²=20²+28²
x²=400+784
x²=1184
x=34.41
x=3441/100
Therefore, the slope that needs to be programmed into the computer to accomplish the delivery is x=3441/100.
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Jacob distributed a survey to his fellow students asking them how many hours they'd spent playing sports in the past day. He also asked them to rate their mood on a scale from 0 00 to 10 1010, with 10 1010 being the happiest. A line was fit to the data to model the relationship.
The best estimate of the average change in mood rating linked with an additional hour spent playing sports is 1.5 points, according to the presented linear function.
Modeling a linear function involves:
y = mx + b
The slope, or m, measures how quickly y changes when x changes by one.
The value of y at x = 0 is represented by the y-intercept, or b.
In the given problem
The amount of time they invested in sports is x.
Their mood score is y.
The required equation is ,
y =1.5 + 5
Given that the slope is m = 1.5, the best estimate of the average change in mood rating resulting from an extra hour spent playing sports is 1.5 points.
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i tried the cosine rule and the sine rule but i dont get why the answer is wrong.
Answer:
93.2° (nearest tenth)
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Sine Rule} \\\\\\$\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c} $\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}[/tex]
From inspection of the given triangle:
B = 38°b = 9 cmc = 11 cmSubstitute the values into the sine rule to find the measure of angle C:
[tex]\implies \dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]
[tex]\implies \dfrac{\sin 38^{\circ}}{9}=\dfrac{\sin C}{11}[/tex]
[tex]\implies \sin C=\dfrac{11\sin 38^{\circ}}{9}[/tex]
[tex]\implies C=\sin ^{-1} \left(\dfrac{11\sin 38^{\circ}}{9}\right)[/tex]
[tex]\implies C=48.80523914...^{\circ}[/tex]
Interior angles of a triangle sum to 180°.
[tex]\implies A+B+C=180^{\circ}[/tex]
[tex]\implies A+38^{\circ}+48.80523914...^{\circ}=180^{\circ}[/tex]
[tex]\implies A=93.19476086...^{\circ}[/tex]
Therefore, the size of angle A is 93.2° (nearest tenth).
help help help help help help help help help help help help help help help help help help help help help hel
1. Which equation represents a line that has a slope of 2 and passes through the origin?
A y=2x
B. y=x+2
C. y x
D. y=-x
A regular jeepney ride costs $12.00 for the first 4 km, and each additional km adds P1.50 to the fare
2. Which of the following can be used to compute a regular fare (F), in pesos, for a 6-km nde?
A. F = 12(7)
B. F=12(7)+1.50
C.=12(150)+7
D.=12+2(1.50)
A regular jeepney ride costs P12.00 for the first 4 km, and each additional km adds P1.50 to the fare
3. How much is the regular fare for a 6-km ride?
A. P15
B. P13.50
C. P14.50
D. P16
4.Which equation represents a vertical line?
A. y =2x
B. x = 2
C. y = 3
D. y = -x
1. Which equation represents a line that has a slope of 2 and passes through the origin?
A y=2x
B. y=x+2
C. y x
D. y=-x
2. A regular jeepney ride costs $12.00 for the first 4 km, and each additional km adds P1.50 to the fare. Which of the following can be used to compute a regular fare (F), in pesos, for a 6-km nde?
A. F = 12(7)
B. F=12(7)+1.50
C.=12(150)+7
D.=12+2(1.50)
3. A regular jeepney ride costs P12.00 for the first 4 km, and each additional km adds P1.50 to the fare. How much is the regular fare for a 6-km ride?
A. P15
B. P13.50
C. P14.50
D. P16
4.Which equation represents a vertical line?
A. y =2x
B. x = 2
C. y = 3
D. y = -x
An equiangular triangle has one side of length six inches. What is the height of the triangle, drawn from that side, to the nearest tenth of an inch?
height = ------------- in.
Answer:
5.2
Step-by-step explanation:
Construct an altitude. Using the Pythagorean theorem, the height is [tex]\sqrt{6^2-3^2} \approx 5.2[/tex]
An art museum gift shop sells prints of a famous painting. The original
painting is 120 cm wide and 85 cm tall. If the print is 50 cm wide, how tall
is the print?
SOLUTION
The print is 35.41 cm tall.
What is Proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
The original painting is 120 cm wide and 85 cm tall.
and, the print is 50 cm wide.
let the print is x cm tall
So, x/ 50 = 85 / 120
120x = 4250
x= 35.41 cm
Hence, the print is 35.41 cm tall.
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Mr. Tull bought 6 videotapes and 5 audio tapes. What is the ratio of videotapes to the total number of tapes?
Answer: 6:11
Step-by-step explanation:
Find the total by 6 + 5 =11
He bought 6 videotapes so ratio is 6:11
Gia is making chocolate truffles. Using the table, find the constant of proportionality
Using the table we find the constant of proportionality is 15/8
What is constant of proportionality?The ratio that establishes a proportionate link between any two given values is referred to as the constant of proportionality. There are also other names for the constant of proportionality, such as constant ratio, constant rate, unit rate, constant of variation, and even rate of change.
Here,
Since from the table we have to find the constant of proportionality
So, the values of ounces of milk(x) are
30,45
and the values of amount of truffle(y) are
16,24
So for finding the constant of proportionality We take 2 cases,
a)Taking first values of x & y
x/y=30/16
x/y=15/8
b)Taking secondary values of x & y
x/y=45/24
x/y=15/8
Therefore the constant of proportionality is 15/8
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Write the equation of the line that goes through the point (4, -7) and is perpendicular to the line
y +6=-2/5(x-1). Use the table to show your work, if needed, to determine each form, and then give each form.
Point-Slope Form
Slope-Intercept Form
Show your work.
The point-slope form with a slope of 5/2 and a point of (4,-7) is 5x-2y=34.
What is line equation?In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10. Linear equations are classified into three types: point-slope, standard, and slope-intercept.
Here,
The slope of line perpendicular to the line y +6=-2/5(x-1)
m1=5/2
point=(4,-7)
y-y1=m(x-x1)
y+7=5/2(x-4)
2y+14=5x-20
5x-2y=34
The point-slope form for slope given as 5/2 and point as (4,-7) will be 5x-2y=34.
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dory orders three soft tacos and three double Deckers for 11.25. Nemo pays 10.00 for four soft tacos and two double Deckers. write a system of equations that represent the lunch orders for dory and Nemo. Use x to represent soft tacos and y to represent double Deckers.
Answer:
Soft tacos are $1.25 each, while double deckers are $2.5 each.
(I didn't have time for a step by step explanation at the moment)
Sorry
8. Model Real Life A window cleaner has cleaned 467 windows
of a skyscraper. He cleans some more. Now there are 967 clean
windows. Each floor of the skyscraper has 100 windows. How
many floors of windows does the window cleaner clean?
The number of floors of windows that the window cleaner cleans will be 10.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
A window cleaner has cleaned 467 windows of a high rise. He cleans some more. Presently there are 967 clean windows. Each floor of the high rise has 100 windows.
The number of floors of windows that the window cleaner cleans will be given as,
⇒ 967 / 100
⇒ 9.67
⇒ 10 floors
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6am air traffic controller i tracking two plane to tart plane A wa at an altitude of 1500 meter and plane B wa at an altitude of 1115 meter plane A i going altitude at 19 meter per econd and plan B wa gaining altitude at 26 meter per econd let x be the number of econd that have pae
At 55 seconds , both the plane A and plane B will have same altitude.
According to the question,
The altitude of plane A = 1500m
The altitude of plane B = 1115m
Altitude plane A gained = 19m/s
Altitude plane B gained = 26m/s
Let "x" be the number of second
Let the equation of plan A and plane B is
a(x) = m₁ x + 1500
b(x) = m₂ x + 1115
We know how fast they are gaining altitude. The are the m values
m₁ = 19
m₂ = 26
So, now we have
a(x) = 19 x + 1500
b(x) = 26 x + 1115
So , to have same altitude ,
a(x) = b(x)
=> 19 x + 1500 = 26 x + 1115
Solving for x,
=> 26x-19x = 1500 - 1115
=> 17x = 385
=> x = 55 seconds
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HELP. ITS AN EMERGENCY. ANSWER WITHIN 20MINS FOR 100 CREDITS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
12: This one if fairy simple: all you need is a line that is not parallel to the line provided, and combined with it, it will provide a solution that's on that line. For example:
y = 2x
x - y = 10
13: Just find two lines that cross (6, -4).
You can use point-slope form:
y - y1 = m(x-x1)
y + 4 = m(x - 6)
then choose two equations with different m's
y = 2(x-6) - 4
y = 3(x-6) - 4
14:
Line one has a slope of two and an intercept at y=0 so it is y = 2x
Line two has a slope of one and an intercept at y=-1 so it is y = x - 1
To find the solution of the system, substitute y:
2x = x - 1
x = -1
Then plug back in:
y = 2 * -1 = -2
So the solution is: (-1, -2)
PLEASE HELP ITS GEOMETRY ASAP HELP ME
50 POINTS IF ANSWERED!!!!
Find the value of x
Answer:
The answer is 45
Step-by-step explanation:
the way to find this answer is by, first, knowing that each angle of a triangle adds up to 180. So, we must first add the 85 and 50 which will give us 135. After, you subtract it all from 180, which gives you 45.
In the triangle, the value of x is,
⇒ x = 45°
We have to given that;
In triangle;
The angles are 85 degree, 50 degree and x.
Since, We know that;
Sum of all interior angle of a triangle are 180 degree.
Hence, We get;
⇒ x + 85 + 50 = 180
⇒ x + 135 = 180
⇒ x = 180 - 135
⇒ x = 45°
Thus, the value of x is,
⇒ x = 45°
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2 1/2 + 3 1/5 x 5 5/8
The solution to the expression 2 1/2 + 3 1/5 x 5 5/8 is 223/2
What is Fraction?fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.
2 1/2 + 3 1/5 x 5 5/8 can be solved by converting all the mixed fraction to improper fraction
2 1/2 = 5/2
3 1/5 = 16/5
5 5/8 = 45/8
which reduces it to
5/2 + 45/8 x 16/5
using BODMAS we taking care of the multiplication section first
45/8 x 16/5 = 18
5/2 + 18
18 can be writen as a fraction which is 36/2
5/2 + 36/2 = 41/2
in conclusion the simplified form of the expression is 41/2
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A textbook store sold a combined total of 447 biology and sociology textbooks in a week. The number of sociology textbooks sold was 63 less than the number of biology textbooks sold. How many textbooks of each type were sold?
255 biology and 192 sociology textbooks were sold in a week.
What is linear equation?Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.
While the graph of a linear equation with two variables, x and y, creates a straight line, the graph of a linear equation with just one variable, x, forms a vertical line that is parallel to the y-axis.
Step 1:
Let x be the number of biology textbooks and y be number of sociology textbooks.
x + y = 447 ------(1)
x - y = 63 ------(2)
Step 2:
Adding (1) and (2), we get
2x = 510
x = 255
Step 3:
Subtracting (1) from (2), we get
2y = 384
y = 192
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