To find the effective rate of interest on a 13-week Treasury bill with a 4% rate, you first convert the discount rate to an annualized rate by dividing the time period by the number of weeks in a year. As Treasury bills do not compound within the maturity period, the EAR is simply the annualized rate, which in this case is 16%.
Explanation:To calculate the effective rate of interest for a $10,000 Treasury bill with a 4% interest rate for 13 weeks, we use the formula for the effective annual rate (EAR). The formula considers the nominal annual interest rate and the number of compounding periods per year.
The nominal annual interest rate is given by the face value minus the price paid for the Treasury bill, divided by the price paid, and then multiplied by 100 to get the percentage. However, the question only provides the interest rate but not the purchase price, so I'm assuming this given interest rate is the discount rate. First, we need to calculate the annualized discount rate and then convert it to the effective annual rate since Treasury bills are typically discounted securities.
To calculate the annualized discount rate:
Convert the 13 weeks to a fraction of the year: 13/52 = 0.25 years.Multiply the stated discount rate (4%) by the annualization factor (1/0.25): 4% * (1/0.25) = 16%.Now, to convert the annualized discount rate to the effective annual rate (EAR):
EAR = (1 + nominal interest rate / number of compounding periods) ^ number of compounding periods - 1.Since Treasury bills do not have compounding within their maturity period, the number of compounding periods is 1.EAR = (1 + 0.16 / 1) ^ 1 - 1 = 0.16 or 16%.Note: If the purchase price was lower than the face value to account for the 4% interest over 13 weeks, the effective annual rate would be higher than 16%.
A rectangle is dialated using a scale factor of 6. The image is then dilated using a scale factor of one thirds. What scale factor could you use to dilate the original rectangle to get the final rectangle? Explain
Answer:
If this rectangle is dilated using a scale factor of One-half through point B, what is the result?
Point B is the bottom left corner of rectangle X.
Step-by-step explanation:
Balu and Pumba shared ½ of a cake. Balu got to eat twice as much cake as Pumba. What fraction of the whole cake did Balu eat?
Final answer:
Balu ate 1/3 of the whole cake.
Explanation:
To solve this problem, we can use the concept of fractions. Let's say Pumba ate x fraction of the cake. Then Balu ate twice as much as Pumba, which means Balu ate 2x fraction of the cake. Together, Pumba and Balu ate 1/2 of the cake. So we can add their fractions: x + 2x = 1/2. Combining the like terms, we get 3x = 1/2. To solve for x, we divide both sides of the equation by 3: x = 1/2 ÷ 3 = 1/6. Therefore, Balu ate 2x = 2 × (1/6) = 2/6 = 1/3 of the cake.
A store sells 3 video tapes for $4.99 find the unit rate in dollars per videotape round to the nearest cent
The unit rate of video tape is $1.66.
What is division?One of the fundamental mathematical operations is division, which involves breaking a bigger number into smaller groups with the same number of components.
Repetitive subtraction is the process of division. It operates in the opposite direction of multiplication.
Given cost of 3 video tapes = $4.99
to find the cost of 1 tape,
we can calculate by using division method
cost of 1 tape = 4.99/3
cost of 1 tape = 1.66333
cost of 1 tape = $1.66
Hence the cost is $1.66.
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What is the relationship between 2.57×10^4 and 2.57×10^−1 ? Select from the drop-down menus to correctly complete the statement.
A)1000 B)Greater
10,000 Less than
100,000
1,000,000
Answer:
We have the numbers:
2.57×10^4 and 2.57×10^−1
The first thing we can see is that the first number exponent is 4, and the second number's exponent is -1, so the difference between is of 5.
If we calculate the quotient between the numbers we have:
(2.57×10^4)/( 2.57×10^−1) = (2.57/2.57)*(10^4/10^-1) = 1*10^(4 - (-1)) = 10^5
Then the first number is 10^5 times bigger than the second number, then the first number is 100,000 greater than the second one.
What is the equation of the line shown in this graph?
Drag and drop the expressions to write the equation of the line in slope-intercept form.
y = __ + ___
choices : 4x , 2x , -x , -2x , 2 , 4 , -4 , -2
The equation of line is y = -1/2 x + 5/2 or x+ 2y = 5.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
The points from the Graph are (1, 2) and ( 4, -4).
So, the slope is
= (4-1)/(-4-2)
= 3/(-6)
= -1/2
and, using the slope intercept form
(y- 2)= m (x- 1)
y-2 = -1/2 ( x-1)
y-2 = -1/2x + 1/2
y= -1/2 x + 1/2 + 2
y = -1/2 x + 5/2
2y = -x + 5
x+ 2y = 5
Hence, the equation of line is y = -1/2 x + 5/2 or x+ 2y = 5.
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The "ACTUAL" answer is y = -2x + 4
What is 6² in expanded form?
A. 36
B. 12
C. 2 × 2 × 2 × 2 × 2 × 2
D. 6 × 6
Is it D I'm not sure?
THE BEST ANSWER GETS BRAINLIEST
Jose made some pancakes. For every 6 cups of flour, he added 7 cups of milk. The ratio of flour to milk in Jose's pancakes is____.
which properties are illustrated by these equations?
1/2 times 3/3 =3/6 2/3 times 3/2 =1
Help its due tomorrow!!!
The perimeter of Square A is 24 linear units. The area of Square B is 4 times the area of Square A. What is the area of Square B? What is the perimeter of Square B?show your work
Answer:
area of Square B: 144 quadratic units
perimeter of Square B: 48 linear units
Step-by-step explanation:
The perimeter of a square is
perimeter = 4*L
where L is the length of each square side. For square A:
24 = 4*L
L = 24/4
L = 6 linear units
The area of a square is
area = L^2
For square A:
area = 6^2 = 36 quadratic units
The area of Square B is 4 times the area of Square A. So
area of Square B = 4*area of Square A
area of Square B = 4*36
area of Square B = 144 quadratic units
And the length of the sides of the square B can be computed as
area = L^2
L = sqrt(area)
L = sqrt(144)
L = 12 linear units
Therefore, the perimeter of square B is
perimeter = 4*L
perimeter = 4*12
perimeter = 48 linear units
4. Johnny took a bus 220 miles south to Fort Lauderdale and then 60 miles west to Naples. He flew home. How many miles did he fly home?
Johnny's flight home distance is calculated using the Pythagorean theorem, which comes to approximately 228 miles, treating his southward and westward travels as legs of a right-angled triangle.
Explanation:The question asks about the flight distance Johnny must cover to get home. Since Johnny traveled 220 miles south and then 60 miles west, we can represent this as a right-angled triangle with the southward travel as one leg and the westward travel as the other leg. According to the Pythagorean theorem, which states that in a right-angled triangle the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides, we can calculate Johnny's flight distance home.
Therefore, the calculation would look like this:
Plugging in the numbers:
Johnny's flight distance home is approximately 228 miles.
Last week, Chen bought 812 gallons of gas at $2.30 per gallon. This week, he bought 4310 gallons of gas at $2.70 per gallon.
What was his total cost?
The total cost for the gas that was bought by Chen is $13504.60.
How to calculate the cost?Chen bought 812 gallons of gas at $2.30 per gallon. The cost for the gas will be:
= $2.30 × 812
= $1867.60
This week, he bought 4310 gallons of gas at $2.70 per gallon. The cost will be:
= $2.70 × 4310
= $11637
The total cost will be:
= $1867.60 + $11637
= $13504.60
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Bo paid bills with 1/2 of his paycheck and 1/5 of the reminder in savings. The rest of his paycheck he divided equally among the college accounts of his 3 kids. What fraction of his paycheck went into each child’s account?
Lucio says he can use counters to represent the number of eggs laid. Explain how he could do this to find out whose chickens laid more eggs
Lucio can use counters to represent the number of eggs laid by each set of chickens. He can then compare the numbers to ascertain which set laid more eggs. Counters provide a simple way to visually represent and compare quantities.
Explanation:Lucio can use counters to represent the number of eggs laid by allocating one counter for each egg. Let's assume Lucio has two sets of chickens from which he collects eggs. He can use different colored counters or different objects to represent the eggs laid by each set. Every time a chicken lays an egg, he places a corresponding counter in a designated area. By the end of a certain period, say one day, he can compare the number of counters in each area. This way, the set of chickens with more counters represents the one that laid more eggs.
Counters provide a simple yet effective way to visually represent and compare quantities in real-world scenarios.
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Eva is arranging 24 photos in an album. How many different ways can she arrange the photos so that the number of photos on each page is the same?
Final answer:
To determine how Eva can arrange 24 photos in an album so that each page has the same number of photos, we need to find the factors of 24. With factors of 1, 2, 3, 4, 6, 8, 12, and 24, there are 8 distinct ways to arrange the photos across the album's pages with each page having the same number of photos.
Explanation:
The student's question is about determining the different ways Eva can arrange 24 photos in an album so that each page contains the same number of photos. To solve this, we need to consider the factors of 24, as the number of photos on each page must be a factor of the total number. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. This means Eva has 8 different page arrangements where each page has the same number of photos.
Now, for each of these arrangements, the order of the photos on each page and the order of the pages themselves can change. If we assume all photos are distinct, the number of ways to arrange the photos on a single page is the factorial of the number of photos per page. However, since Eva is concerned only with the arrangement of the number of photos per page being the same, not the order within the pages, we only need to consider the 8 different page arrangements.
HELP ASSAP WITH THIS QUESTION
Which Function rule matches the graph below?
a. f(x) = x
b. f(x) = x-2
c. f(x) = x+2
d. f(x) = 2x
Answer:
Step-by-step explanation:
from ground level to the tip the statue of liberty and its pedestal are 92.99 metars tall. the pedestal is .89 meters taller than the statue. how tall is the statue of iberty
what does the measure of B Equal?
MIA has a rectangle of cloth.she dips the top5/8 of cloth in blue dye.she dips the bottom 9/20 of the cloth in yellow dye.the part of cloth dips in both turns green.wirk out fraction that turns green.
Put these in order from Least to greatest.
-23/6, 8 7/12, √17, 8.6, 3√12, -2.18
For the line y = 2/3x, if the y-coordinate is 14, what is the x-coordinate?
A. 7
B. 14
C. 21
D. 3/2
(I think it's 21, show your work, don't answer unless you're 100% sure.)
5,253 divided bye 101
In performing the division of 5,253 by 101, the result comes out to be 52 with a remainder of 1.
Explanation:The student's question is asking for the result of dividing 5,253 by 101. To perform this division, you can use long division method.
Here's how you do it:
Write 5253 and 101 in a division bracket, with 5253 inside and 101 outside. To start, determine how many times 101 goes into 5253. This gives us 52 times.Multiply 101 by 52, which gives 5252. Subtract this from 5253 to get the remainder, which is 1.As we reached a remainder of 1, the division ends here and the final answer comes out to be 52 with a remainder of 1.This implies that 5,253 divided by 101 equals 52 with a remainder of 1.
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Use the distributive property to expand the expression. 5(4r2 + 8s2) − (−3s + 5t)
Answer:
20r^2 + 40s^2 + 3s - 5t just took quiz
Step-by-step explanation:
A bird flew from the ground onto a tree branch 5 feet above the ground. What could the bird do next that would make this situation a model of combining a number and its additive inverse?
A.
Fly down 5 feet and return to the ground.
B.
Fly 5 feet higher up onto another tree branch.
C.
Fly to a different tree branch 5 feet above the ground.
D.
Fly into an empty swimming pool 5 feet below ground level.
Answer:
Fly down 5 feet and return to the ground.
Step-by-step explanation:
We are given that A bird flew from the ground onto a tree branch 5 feet above the ground.
We are supposed to find What could the bird do next that would make this situation a model of combining a number and its additive inverse
Additive inverse - What you add to a number to get zero is additive inverse.
The negative of a number.
Now we are told What could the bird do next that would make this situation a model of combining a number and its additive inverse
Since it already flew 5 feet above the ground .
Additive inverse of 5 feet is -5 feet
So, to make the situation of combining a number and its additive inverse
Bird has to flew 5 feet return to the ground i.e.-5 feet
So, a model of combining a number and its additive inverse = 5+(-5)
Hence Option A is correct.
Fly down 5 feet and return to the ground.
Answer:
A is correct
Step-by-step explanation:
Please Help:
Reaner Recycling collected 7/4 ton of aluminum last Saturday. If 7/8 ton of aluminum can be shredded each day, how many days will it take to process what was collected on Saturday?
To tie-die on T-Shirt, 3/8 cup of dye is needed. The table shows the number of cups each color of die in Mr. Rodriguez's art class. How many T-Shirts will each flower bed contain.
Amount of dye
Color Number of cups
Red 12
Orange 3/4
Natasha is setting tiles along the baseboard in her bathroom. One side of the bathroom is 18 3/4 feet. Each tile is 1 1/2 feet long.
It will take 2 days to process the aluminum collected on Saturday. Each cup of dye can make 1/2 T-Shirt. Each flower bed can make 6 T-Shirts.
Explanation:Mathematics: Middle SchoolTo determine how many days it will take to process the aluminum collected on Saturday, we can divide the amount collected by the amount processed each day.
7/4 ton / 7/8 ton/day = (7/4) / (7/8) = 7/4 x 8/7 = 2 days.
Therefore, it will take 2 days to process the aluminum collected on Saturday.
To find out how many T-Shirts each cup of dye can make, we can divide the amount of dye needed for a T-Shirt by the amount of dye in each cup.
3/8 cup / (3/4) cup = (3/8) / (3/4) = 3/8 x 4/3 = 1/2 T-Shirt.
Therefore, each cup of dye can make 1/2 T-Shirt.
To find out how many T-Shirts each flower bed can make, we need to multiply the amount of dye in each color by the number of cups.
Red: 12 cups x 1/2 T-Shirt = 6 T-Shirts.
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This is a ratio brain teaser}} There are 4 suns and 6 moons. Write the simplest form that compares the numbers
GOOD LUCK!
The simplest form that compares the numbers 4 and 6 is 2:3.
Explanation:To write the simplest form of a ratio, we need to find the greatest common divisor (GCD) of the given numbers and divide both the numerator and denominator by it. In this case, the GCD of 4 and 6 is 2, so we divide both numbers by 2 to get the simplest form of the ratio. Therefore, the simplest form that compares the numbers 4 and 6 is 2:3.
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What is missing for the following quantity to be true? 2x*5a*7 = 5a*2x*__
A. 5a
B. 2x
C. 7
D. 14
Thanks guys!
both sides have 2x & 5a, so both sides need 7
answer is C. 7
Jeff bought a refrigerator for $1,300 he made a 10% down payment and finance the rest at 6% for one year how much interest did he pay?
It takes 3/4 yards of ribbon to make a bow how much ribbon is needed to make 7 bows
Sandy is upgrading her internet service. Fast internet charges $60 for installation $50.45 per month. Quick internet has free installation but charges $57.95 per month write an equation that can be used to find the number of months for which the internet service would cost the same?