Using compound interest, the rates per compounding period are given as follows:
a) 0.1273 = 12.73%.
b) 0.0833 = 8.33%
c) 0.0617 = 6.17%
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year.The interest rate per compounding period is given as follows:
[tex]\left(1 + \frac{r}{n}\right)^n - 1[/tex]
For item a, the parameters are:
r = 0.12, n = 52.
Hence:
[tex]\left(1 + \frac{0.12}{52}\right)^{52} - 1 = 0.1273[/tex]
For item b, the parameters are:
r = 0.08, n = 104.
Hence:
[tex]\left(1 + \frac{0.08}{104}\right)^{104} - 1 = 0.0833[/tex]
For item c, the parameters are:
r = 0.06, n = 12.
Hence:
[tex]\left(1 + \frac{0.06}{12}\right)^{12} - 1 = 0.0617[/tex]
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distribute the problem
2(3-8y)
Answer:
6-16yStep-by-step explanation:
Hello!
apply distributive law
[tex]a(b - c) = ab - ac[/tex]
2(3-8y)=2.3-2.8y
2.3=6-2.8y= -16y=6-16y
Hope it helps!
A phone company surveys a sample of current customers to determine if they use their phones most often to text or use the Internet. They sort the data by payment plans, as shown below. Plan A: 27 text, 21 Internet Plan B: 13 text, 10 Internet Answer the questions to determine a conditional probability. How many customers are on payment plan B? customers How many of the customers on plan B text? customers What is the probability that a randomly selected customer who is on plan B uses the phone most often to text? Give the answer in fraction form.
Answer:
23 customers on payment plan B
13 customers on plan text B
Probability: 13/23
Step-by-step explanation:
Which of the following equation is an example of inverse variations?
f(x) = -1/ 3x and f(x) = -z/xy are both examples of inverse variations. Option B
What are inverse variations?
Inverse variation can be defined as the relationships between variables represented in the form of y = k/x
where;
x and y are two variables k is the constant valueFrom the options given, we can see that;
f(x) = -1/ 3x
f(x) = -z/xy
Both take the form of inverse variations
Thus, f(x) = -1/ 3x and f(x) = -z/xy are both examples of inverse variations. Option B
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what are these questions i need help
177
3 is a root of f(x) = x2–93987. Find the other roots of f(x).
Write your answer as a list of simplified values separated by commas, if there is more than one value.
The roots of the equation f(x) = x^2 - 93987 are x = √93987 and x = -√93987
What are quadratic equations?Quadratic equations are equations that have a second degree and have the standard form of ax^2 + bx + c = 0, where a, b and c are constants and the variable a does not equal 0
How to determine the other roots of the equation?The equation of the function is given as:
f(x) = x^2 - 93987
The above equation is a quadratic equation
Express the equation as a difference of two squares
f(x) = (x - √93987)(x + √93987)
Set the equation of the function to 0
(x - √93987)(x + √93987) = 0
Split the factors of the above function equation as follows
x - √93987 = 0 and x + √93987 = 0
Solve for x in the above equations
x = √93987 and x = -√93987
Hence, the roots of the equation f(x) = x^2 - 93987 are x = √93987 and x = -√93987
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________ is the number of defects in a sample divided by the number of opportunities while ________ is the number of defects divided by the number of units tested within a sample.
DPU is the number of defects in a sample divided by the number of opportunities while DPMO is the number of defects divided by the number of units tested within a sample. Option B
What is DPU?Defects per unit (DPU) can be defined as the number of defects divided by the number of opportunities
It is also seen as the universal measure of quality.
For example, if there are 100 defects in 1,000 units produced, then the defects per unit will be 0.01.
Defects per million opportunities can be defined as a mathematical calculation of the estimated quality of a process
From this information, we can conclude that DPU and DPMO are measure of defects in a sample.
Thus, DPU is the number of defects in a sample divided by the number of opportunities while DPMO is the number of defects divided by the number of units tested within a sample. Option B
Complete question is;
________ is the number of defects in a sample divided by the number of opportunities while ________ is the number of defects divided by the number of units tested within a sample.
a. DPMO, DPU
b. DPU, DPMO
c. RTY, FTY
d. FTY, RTY
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Find the distance between the given points.
R(O, O) and S(6, 8)
Distance =
Answer:
distance = 10
2/7 /(22) = 10
x - 2y = 3
5x + 3y = 2
The lines whose equations are shown intersect at which point?
The point of intersection of the two lines is at (1,-1)
System of equationThe given system of expression is shown below
x - 2y = 3
5x + 3y = 2
The solution to the system of equation is the point of intersection
From equation 1
x = 3 + 2y
Substitute into 2
5(3+2y) + 3y = 2
15 +10y + 3y = 2
13y = -13
y = -1
Substitute y = -1 into 3
x = 3 + 2y
x = 3+(-2)
x = 1
Hence the point of intersection of the two lines is at (1,-1)
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The diameter of a circle is 8 mm. What is the circumference of the circle?
25 and 1/7mm?
50 and 2/7mm?
11/28mm?
Or
19 and 1/4mm?
Answer:
25.12 rounded.
Step-by-step explanation:
C = 2[tex]\pi[/tex]r
C=[tex]\pi[/tex]d
C = [tex]\pi[/tex](8)
C = 25.12 rounded.
Answer:
25 and 1/7 mm
Step-by-step explanation:
Diameter = circunference / π
π = 3.1416 aprox.
Then:
8 = citcunference / 3.1416
8 * 3.1416 = circunference
25.1428 = circunference
1/7 = 0.1428
Then:
25.1428 = 25 + 1/7
= 25 1/7
The following are the ages of 13 history teachers in a school district. 24, 27, 29, 29, 35, 39, 43, 45, 46, 49, 51, 51, 56 Notice that the ages are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set.
Answer:
Below in bold.
Step-by-step explanation:
Minimum 24
Lower quartile 29
Median 43
Upper quartile = (49 + 51) / 2 = 50
Maximum = 56
Interquartile range = 50-29 = 21.
Which of the following graphs has a zero correlation?
Select the correct answer.
Which equation represents the vertical line passing through (14.-16)?
OA
OB. y=-16
OC
X= 14
OD.
y=14
X=-16
Check the picture below.
Instructions: Find the missing side length in the image below.
? =
10/
7
?
14.
Using proportions, the missing side length in the image below is of 20.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
In this problem, the side lengths are proportional, being related by the rule of three given as follows:
x/10 = 14/7
Applying cross multiplication:
7x = 14 x 10
7x = 140
x = 140/7
x = 20.
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a 36 foot long pole is cut into two pieces with the ratio lengths equal to 5:7
what is the lengh of the longer piece?
Question is in image below:
The sinusoidal equation will be Y=4.25 sin[(π/26)(t-11)]+12.25
How to compute the equation?The following can be deduced:
Function Y=Asin(wt-Φ)+β
Amplitude A=(16.5-8)/2=4.25 hours
Vertical shift β= (16.5+8)/2=12.25
Period is 52 weeks, thus 52=2π/ω→ω=2π/52=π/26
The phase shift Φ can be gotten if we divide the whole year in 4 sub-intervals each interval would be :
[0,13], [13,26],[26,39],[39,52]
The summer solstice occurs at the end of week 24.
The winter solstice occurs at the end of week 51.
The maximum of sine function happens at the end of the first sub-interval [0,13]
Here, Φ is 11, thus, the function would be
Y=4.25 sin[(π/26)(t-11)]+12.25.
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A puppy weighed 2kg.
Eight weeks later the puppy weighed 3.5kg
What was the percentage increase in the puppy's weight?
Answer:
[tex]3.5 - 2 \times 100 \div 2[/tex]
Answer:
The percentage increase in the puppy's weight is 75%.
Step-by-step explanation:
We can find the percentage increase using the following formula:
[tex]\boxed{\% \space\ \mathrm {increase = \frac{final \space\ - \space\ initial}{initial} \times 100}}[/tex].
In this case,
• initial = 2 kg
• final = 3.5 kg
Substituting these values into the formula:
[tex]{\% \space\ \mathrm {increase = \frac{3.5 \space\ - \space\ 2}{2} \times 100}}[/tex]
⇒ [tex]\frac{1.5}{2} \times 100[/tex]
⇒ [tex]0.75 \times 100[/tex]
⇒ 75%
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
[tex] \sqrt{112x {}^{6}y {}^{3} {z}^{5} } \\ \sqrt{(2 {}^{4} \times 7 )x {}^{6}y {}^{2}yz {}^{4} z } \\ 2 {}^{2}x {}^{3} yz {}^{2} \sqrt{7yz} [/tex]
Last optionpls help me solve these
The conversion of 9.204 to a mixed number will be 9 51/250.
How to illustrate the information?It should be noted that converting decimal to mixed numbers simply means changing them to whole numbers and fractions.
Therefore, 9.204 will be:
= 9 204/1000
= 9 51/250
The percentage equivalent of 3 7/8 will be:
= (3 × 100) + (7/8 × 100)
= 300 + 87.5
= 387.5%
Dividing 72 in the ratio 2:3:4 will be:
= 2/9 × 72 = 16
= 3/9 × 72 = 24
= 4/9 × 72 = 32
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A car is traveling at vx = 36 m/s. the driver applies the brakes and the car decelerates at ax = -6. 0 m/s2. what is the stopping distance?
Answer:
6 Meters
Step-by-step explanation:
If the car is driving at a constant velocity of 36 m/s and accelerates at -6.0 m/s ^2 to a stop, then the distance of the car decelerates to a stop in 6 seconds.
a=v/t ->>> 6= 36/t
Please help I need an answer
The midpoint of the given line in coordinate form (x, y) is -0.5, 0)
Midpoint of a lineThe midpoint of a line is the middle of the given line. Given the coordinate points (x1, y1) and (x2, y2), the midpoint of the line is given as:
M(x, y) = {x1+x2/2, y1+y2/2}
Given the coordinate points on the line (-2, 1) and (1, -1)
Substitute the given coordinate points into the formula to have:
M(x, y) = {-2+ 1/2, 1-1/2}
M(x, y) = {-1/2, 0/2}
M(x, y) =(-0.5, 0)
Hence the midpoint of the given line in coordinate form (x, y) is (-0.5, 0)
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The probability for event A is 0.3, the probability for event B is 0.6, and the probability of events A or B is 0.8.
Why are the events not mutually exclusive
The events are not mutually exclusive because P(A or B) is not equal to P(A) + P(B)
Why are the events not mutually exclusive?The probability values are given as:
P(A) = 0.3
P(B) = 0.6
P(A or B) = 0.8
For mutually exclusive events, we have:
P(A or B) = P(A) + P(B)
Substitute the known values in the above equation
P(A or B) = 0.3 + 0.6
Evaluate the sum
P(A or B) = 0.9
From the given parameters, we have
P(A or B) = 0.8
Hence, the events are not mutually exclusive because P(A or B) is not equal to P(A) + P(B)
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Answer:
D
Step-by-step explanation:
edge 2023
The sum of P(A) and P(B) is not equal to P(A or B).
Erin’s car uses 6 gallons of gas for every 138 miles she drives. Which equation could be used to find how many gallons,g, Erin needs to drive 92 miles
Answer:
g = 6 / 3 x 2
Step-by-step explanation:
g = 6 / 3 x 2 because 92 / 2 = 46. 46 x 3 = 138. so / 3 = 46 x 2 = 92
Thus, Erin required 4 gallons of gas to drive 92 miles.
What is proportionality?proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense that are they directly proportional or inversely proportional to each other.
Let the gallon used by Erin bey and distance traveled be x
Now fuel consumed by Erin is directly proportional to the distance traveled i.e.
y ∝ x
y = ax - - - - - - (1)
where is the constant
Now put y = 6 and x = 138
6 = a * 138
a = 6/138
a = 0.043
Now put a in equation 1
y = 0.043x
The above expression is a required expression that implies how mush gallons of gas Erin used to travel a certain distance.
Erin needs to drive 92 miles,
Put x = 92 in above expression
y = 0.043 * 92
y = 4 gallon
Thus, Erin required 4 gallons of gas to drive 92 miles.
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3. What kind of triangle is represented by the triangle shown below?
Isosceles
Right
O Equilateral
Scalene
Answer:
Isosceles
Step-by-step explanation:
An Isosceles triangle has an acute angle (less than 45°), and this photo shows a triangle with two matching sides with one side being longer.
A right triangle would have a 90° angle which this photo doesn't have
An Equilateral triangle has all 60° sides, since it doesn't have all matching sides, it cannot be the answer.
A Scalene triangle is similar to this photo except it has 30° 60° and 90° angles, which this photo doesn't have.
I hope this helps!
Consider this function. f(x)=6log2x-3 over which interval is function f increasing at the greatest rate?
The function increased at the highest rate in the interval [1/8, 1/2], as can be seen from the function value and its interval values.
What is maxima and minima?A function's maxima and minima are its highest and lowest values, respectively, either on the entire domain or inside a certain range. They are referred to as the function's extrema collectively. The plural forms of maximum and minimum for a function are respectively known as maxima and minima.
Why do we use maxima and minima?The extreme values of a function—their maximum and minimum values—are referred to by the words maxima and minima. Maximum refers to the maximum value or amount that is feasible. A function's biggest value within its range is known as its absolute maximum.
According to the given information we have:f(x)=6log2x-3
For the interval x ∈[2, 6]
f(x) ∈ [-0.678, 3]
For the interval x ∈ [1/8, 1/2]
f(x) ∈ [ -9.96, -5.32]
For the interval x ∈ [1, 2]
f(x) ∈ [-3, -0.67]
For the interval x∈ [1/2, 1]
f(x) ∈ [-5.32, -3]
The function increased at the highest rate in the interval [1/8, 1/2], as can be seen from the function value and its interval values.
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These cones are similar. Find the volume
of the smaller cone. Round to the
nearest tenth.
2 cm
Volume = [?] cm³
3 cm
Volume = 66 cm³
Answer:
Hight = 22 cm
Volume of BlueCone= 92 [tex]cm^2[/tex]
Step-by-step explanation:
Finding the Hight of The Red Cone(Check the Image)
Volume of The Blue Cone(Check Image Below)
Use the wave equation to find the speed of a wave given by y(x,t) = (9. 13 mm) sin[(6. 65 m-1)x - (5. 52 s-1)t]
The speed of the wave is 0.83 m/s.
According to the statement
we have given that the equation and we have to find the speed of the wave.
So, For this purpose, we know that the
The given equation is y(x,t) = (9. 13 mm) sin [(6. 65 m^-1)x - (5. 52 s^-1)t]
Then we have to find the speed of the wave
So, Comparing y(x,t) = (9. 13 mm) sin[(6. 65 m-1)x - (5. 52 s-1)t]
to the general expression y(x,t)=y m sin(kx−ωt),
Because the general expression is y(x,t)=y m sin(kx−ωt)
we see that k= 6.65 m −1 and ω= 5.52 rad/s.
The speed of the wave is
v=ω/k=(5.52 rad/s)/(6.65 m )= 0.83 m/s
So, The speed of the wave is 0.83 m/s.
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A regular decagon with exterior angle 1 is shown.
In the regular decagon shown, what is the measure of angle 1?
°
Answer:
∠1 = 36°
Step-by-step explanation:
All angles of a regular polygon are congruent, as are the sides. A regular decagon will have 10 congruent angles.
Exterior anglesThe sum of the measures of the exterior angles of a convex polygon is always 360°. This decagon has 10 congruent exterior angles, so the measure of each is given by ...
10(∠1) = 360°
∠1 = 36° . . . . . . . . divide by 10
Answer: 36°
Step-by-step explanation: Trust Me!
Answer is correct on Edge. Good Luck! :)
In the regular decagon shown, what is the measure of angle 1?
36°360° is always the sum of all measures of all exterior angles of a convex polygon. A decagon have 10 sides.
Since ∠1 = 36°, then each other angle should measure the same, 36°.
In order to know whether the sum of all the angles equal 360°,
we need to multiply: 36° x 10.
36° x 10= 360°.
And sure enough the answer is correct.
Help help help help help help
Answer:
∠JKL = 98
Step-by-step explanation:
the two small vertical lines on JK & KL means that
JK & KL are the same length which means that
same length means same degrees
∠KJL & ∠KLJ are the same degrees
∠KJL & ∠KLJ are both 41 degrees
triangles are 180
41 + 41 = 82
180 - 82 = 98
1) The ratio of the number of Mary's stickers to Anne's is 4:7. Mary has 48 stickers. If
Mary buys another 8 stickers, what will be the new ratio of the number of Mary's
stickers to Anne's?
Answer:
2:3
Step-by-step explanation:
ratio = 4:7
4 parts = 48
1 part = 12
Mary has 48
Anne has 84
Mary will have 56
56:84 = 2:3
A soccer team ordered 12 jerseys and 12 pairs of shorts, for a total of $156. Later, they had to order 4 more jerseys and 6 more pairs of shorts, for a total of $62.
The system of equations that can be used to find x, the cost of each jersey, and y, the cost of each pair of shorts is shown.
12x + 12y = 156
4x + 6y = 62
What is the cost of each jersey?
The cost of each jersey is $8 dollar and that of shorts is $5
System of equationThis are expression that contain unknown equation and two or more equation.
According to the question, a soccer team ordered 12 jerseys and 12 pairs of shorts, for a total of $156. Later, they had to order 4 more jerseys and 6 more pairs of shorts, for a total of $62.
The system of equation that represent the expression is given as;
12x + 12y = 156
4x + 6y = 62
____________
6x + 6y = 78
4x + 6y = 62
Subtract
6x-4x = 78 - 62
2x = 16
x = 8
since 4x + 6y = 62
2x+3y = 31
2(8) + 3y = 31
3y = 31-16
3y = 15
y = 5
Therefore the cost of each jersey is $8 dollar and that of shorts is $5
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Noah has 22 5 of a pound of rice in his cupboard. He also has 8 9 of that amount in his pantry. Which of the following equations could be used to determine how much rice he has in the pantry?
225/0.88*100%
255.68*100
25,568 pounds in pantry