Tree diagrams are a helpful tool for calcuating probabilities when there are several independent events involved. They get their name because these types of diagrams resemble the shape of a tree. The branches of a tree split off from one another, which then in turn have smaller branches. Just like a tree, tree diagrams branch out and can become quite intricate.
Assume the $10,000 Treasury bill, 4% for 13 weeks. Calculate the effective rate of interest
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%.
what is the volume of 20 grams of an object with a density of 55g/cm^3?
The volume of an object with a mass of 55g/cm³ and a mass of 20 grams is 27.5cm³.
What are mass, volume, and density?Mass is the quantity of matter in a physical body.
The volume shows the amount of 3D space occupied by a closed object.
Density is mass per unit of volume.
Volume is only defined for 3-dimensional objects 2 dimensional objects have no volume.
We know volume is equal to mass/density.
Given an object has a density of 55g/cm³ and a mass is 20 grams.
∴ Volume = (55/20) cm³.
learn more about volume here :
https://brainly.com/question/13338592
#SPJ2
is 4.47 a rational number
Yes, 4.47 is a rational number because it can be expressed as a fraction of two integers.
Explanation:Yes, 4.47 is a rational number.
A rational number is a number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero.
In this case, we can express 4.47 as the fraction 447/100, which is a quotient of two integers. Therefore, it is a rational number.
Learn more about rational numbers here:https://brainly.com/question/24398433
#SPJ2
Tammy and Jodi assembled 420 circuit boards in 8 hours. The next day they assembled 36 more circuit boards in the same amount of time. What was their average rate on the second day? A. 87 boards per hour B. 70 boards per hour C. 57 boards per hour D. 36 boards per hour
Answer:
C
Step-by-step explanation:
Which measure of central tendency best describes this situation: the ages of students in an eighth-grade class?
a) Mean; there likely are no outliers.
b) Mode; the data are not numerical.
c) Median; there likely are outliers.
d) Median; there likely are no outliers.
Answer:
Step-by-step explanation:
Its B=median
Susie is an organic vegetable grower the perimeter of her rectangular vegetable garden is 72 yards the width of the vegetable garden is 9 yards how long is the vegetable garden
A spider walks about 19 cm each second. About how long would it take the spider to walk around the perimeter of a room that is 3 m wide and 4 m long?
Final answer:
To calculate the time it takes the spider to walk around the perimeter of a 3 m by 4 m room, we first find the perimeter in meters, convert it to centimeters, and then divide by the spider's speed in cm/s. The perimeter of the room is 14 m, which is 1400 cm. Dividing this by the spider's speed, 19 cm/s, gives us approximately 74 seconds.
Explanation:
To find out how long it would take the spider to walk around the perimeter of a room that is 3 m wide and 4 m long, we first need to calculate the perimeter of the room. The formula for perimeter P of a rectangle is P = 2(l + w), where l is the length and w is the width.
So for a room that is 3 m wide and 4 m long, the perimeter is:
P = 2(4 m + 3 m) = 2(7 m) = 14 m
Since the spider walks 19 cm each second and there are 100 cm in a meter, we convert the perimeter to centimeters:
14 m = 1400 cm
Now, we calculate the time t it will take for the spider to walk this distance by dividing the perimeter by the spider's speed:
t = perimeter/speed = 1400 cm / 19 cm/s
Therefore, the time taken for the spider to walk around the perimeter is approximately:
t = 73.68 s
So, the spider would take about 74 seconds to walk around the perimeter of the room.
Final answer:
To determine the time for a spider to walk around a 3 m by 4 m room, calculate the perimeter (14 m), convert it to centimeters (1400 cm), and divide by the spider's speed (19 cm/s), resulting in approximately 73.68 seconds.
Explanation:
To calculate the time it would take for a spider to walk around the perimeter of a 3 m by 4 m room, first, find the perimeter of the room by adding the lengths of all the sides:
Perimeter = 2 × (3 m) + 2 × (4 m) = 6 m + 8 m = 14 m.Next, since the spider walks 19 cm each second, convert the perimeter from meters to centimeters because the units need to match.
Perimeter in centimeters = 14 m × 100 cm/m = 1400 cm.Now, divide the total perimeter by the spider's speed to find the time it takes:
Time = Perimeter / SpeedTime = 1400 cm / 19 cm/sTime ≈ 73.68 secondsTherefore, it would take approximately 73.68 seconds for the spider to walk around the perimeter of the room.
In one weekend,a theatre sells 74,877 tickets to a new movie. Write the values for each of the 7s in 74,877.
Answer:
Given number,
74, 877
Since, the place value chart,
Ones = 1,
Tens = 10,
Hundred = 100,
Thousand = 1000,
Ten thousand = 10,000
Hundred thousands = 100,000
Millions = 1,000,000
Hence, by the above chart,
For the number,
74,877
Place value of 7 at ones place = 7,
Place value of 7 at tens place = 70,
Place value of 7 at ten thousand place = 700,000
Is 17 1/2 to the right or left of 17 2/3 on the number line? Explain your answer.
[tex]17\frac{1}{2}[/tex] lies to the left of the number line [tex]17\frac{2}{3}[/tex]
What is number line?A number line can be defined as a pictorial representation of numbers on a straight line.
Given that, Is 17 1/2 to the right or left of 17 2/3 on the number line
17 1/2 = 17.5
17 2/3 = 17.66
17.5 < 17.66
Hence, [tex]17\frac{1}{2}[/tex] lies to the left of [tex]17\frac{2}{3}[/tex]
For more references on number line, click;
https://brainly.com/question/13425491
#SPJ2
Evaluate 12x−3y12x−3y when x=−14x=−14 and y=3y=3.
Answer:
-12
Step-by-step explanation:
I think I got it right on Big Ideas
If a stereo is sold for $59.99 and Karen pays $64.19 for it when she checks out, what is the sales tax in the area
The sales tax in the area where Karen bought the stereo is $4.20. This was calculated by subtracting the original price of the stereo ($59.99) from the total price paid ($64.19).
Explanation:To find the sales tax in this scenario, we need to subtract the original price of the stereo, which is $59.99, from the total price that Karen paid, which is $64.19. The difference will represent the sales tax that Karen had to pay at the checkout.
So we calculate: $64.19 - $59.99 = $4.20
Therefore, the sales tax that Karen paid for the stereo is $4.20.
Learn more about sales tax here:https://brainly.com/question/29442509
#SPJ3
Which number is equal to 10 to the 3rd power
Your picture of your family crest is 4.5 inches wide. You need a reduced copy for the front page of the family newsletter. The copy must fit in a space 1.8 inches wide. Which scale factor should you use on the copy machine to adjust the size of your pictures of the crest?
A) 2/5
B) 5/2
C) 1/2
D) 1/5
Answer:
The answer is : A 2/5
(I just finished taking the test)
The scale factor would be 2/5 to reduce the width from 4.5 inches to 1.8 inches.
What is a scale factor?A scale factor is defined as the ratio of the scale of a given original object to the scale of a new object that is its representation but of a different size (bigger or smaller). For example, we can enlarge a rectangle with sides of 2 cm and 4 cm by multiplying each side by a number, say 2.
Given that your picture of your family crest is 4.5 inches wide. You need a reduced copy for the front page of the family newsletter. The copy must fit in a space 1.8 inches wide.
The scale factor will be calculated as,
Scale factor = Reduced size / Original size
Scale factor = 1.8 / 4.5
Scale factor = 0.4 or 2/5
To know more about scale factors follow
https://brainly.com/question/2826496
#SPJ2
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?
Answer:
Balu ate [tex]\frac{1}{3}[/tex]fraction of the whole cake
Step-by-step explanation:
Let x be the amount of cake eaten by Pumba
Balu got to eat twice as much cake as Pumba.
Balu eat cake = 2x
Balu and Pumba shared ½ of a cake.
So, [tex]2x+x=\frac{1}{2}[/tex]
[tex]3x=\frac{1}{2}[/tex]
[tex]x=\frac{1}{6}[/tex]
So, Pumba's share = [tex]\frac{1}{6}[/tex]
Balu's share = 2x = [tex]\frac{2}{6}=\frac{1}{3}[/tex]
Hence Balu ate [tex]\frac{1}{3}[/tex]fraction of the whole cake
Jeanette and Leslie are trying to solve this problem: A camp counselor has a list of 134 campers who signed up for art class. The counselor can place 8 students in each class. How many classes does the counselor need to have?
*Please Show Work*
Ling uses 21 bananas to make 7 fruit smoothies. What is the unit rate that Ling uses for bananas per each smoothie? What is the unit rate? Explain how to use equivalent fractions to find the answer
Answer:
The unit rate that ling uses for bananas per each smoothie is (3/1) bananas per smoothie
Step-by-step explanation:
Ling uses 21 bananas to make 7 fruit smoothies. Total of bananas B = 21. Total of smoothies S =7.
The unit rate U is the relationships B divided by S.
U = B/S
U = 21 bananas / 7 smoothies
U = 21/7 Bananas per smoothies.
We can use the equivalent fractions to find the unit rate. 21 can be expressed as 7*3. 7 can be expressed as 7*1. We can simplify the number 7 in numerator and denominator.
U = (7*3)/(7*1)
U = 3/1.
Finally, the unit rate is 3/1 bananas per smoothie.
Which scatter plot shows a negative nonlinear association?
Answer:
The second option
Step-by-step explanation:
The answer is the second option because you can clearly see that it is nonlinear since there is no straight line, but you can still see it going at a negative rate.
Does 17/20 repeat or terminate
write the numerical expressions in words then solve 10×(2.5+13.5)
7/2 as an improper fraction
jamil has 3 pet lizards. the pet store owner said that jamil will need to buy a total of 36 crickets to feed his lizards if each lizard eats the numberbof crickts how many crickts does each lizard eat?
I need help with this asap right now please
how to find the answer to this
5g=230 HOW DO I FIND THIS PLZ HELP NOW
A newly discovered planet has a mass of 4.8743 · 10 ^22 kilograms. It's estimated that there is water on the surface and that, the water's mass is only 4 · 10^ -2 percent of the planet's total mass. Use scientific notation to estimate the mass of the planet's water. In your final answer, include all of your estimates and calculations.
To estimate the mass of water on the planet with a mass of 4.8743 × [tex]10^{22[/tex] kg, you multiply this mass by[tex]4 * 10^{-2[/tex] percent converted to decimal (0.0004), giving a water mass of approximately 1.95 * [tex]10^{19[/tex]kg.
To estimate the mass of the planet's water, we first need to find 4% of the planet's total mass. We can do this by multiplying the planet's mass by the percentage as a decimal:
Mass of water = (4.8743 × 10^22 kg) × 0.04
Now, let's perform the multiplication:
Mass of water = 1.94972 × [tex]10^{19[/tex] kg
So, the estimated mass of the planet's water is approximately 1.95 × [tex]10^{19[/tex] kilograms.
Pls help me I really need it
PLEASE HELP!
Sarah paints a straight line. The line is 13 1/2 ft long. She wants to divide the line into sections that are each 1/8 ft long. How many sections will the line be divided into?
A film set designer is using white and colored tiles in a pattern to create paths of different lengths. If x is the length of the path in feet, the number of colored tiles needed to make it is calculated using the rule
(4x2y3)(3x2y2)
where y represents the number of white tiles.
Which simplified expression represents the number of colored tiles used for a path of length x feet?
7x4y5
7x4y6
12x4y5
12x4y6
The simplified algebraic expression for the number of colored tiles used for a path(4x^2y^3)(3x^2y^2), is 12x^4y^5. Hence the correct option is 3,
Given the algebraic rule for determining the number of colored tiles ((4x2y3)(3x2y2)), we simplify this expression by multiplying the coefficients and then by adding the exponents for x and y (since they are the same base).
Multiply the coefficients: 4 x 3 = 12
Add the exponents for x: 2 + 2 = 4 (since x2 x x2 = x2+2)
Add the exponents for y: 3 + 2 = 5 (since y3 x y2 = y3+2)
Jodi went 54 miles on 3.5 gallons of gas, and she wants to know how far she can go on 9 gallons of gas. Which proportion would be useful to solve the problem?
A)
9
3
=
54
x
B)
9
54
=
x
3
C)
54
3.5
=
x
9
D)
54
9
=
3.5
x
Is 632 a multiple of 4
How many times can 4 go into 69