Answer:
$133.2
Step-by-step explanation:
[tex]\frac{120*2*5.5}{100\\}[/tex]=13.2
13.2+120
133.2
The simple interest of$13.2 is due on loan of $120 for two years with the annual rate of 5.5%.
What is simple interest?simple interest is the interest amount for a particular principal amount of money at some rate of interest.
Simple interest formulaS.I = (P × R × T)/100
Where,
S.I is simple interest
P is the Principal amount
R is the interest rate
T is time in years
According to the given question.
We have
Principal, P = $120
Interest rate, R = 5.5%
And time, T = 2 years
Therefore, the simple interest for two years for the amount $120 is given by
[tex]S.I = \frac{(120)(5.5)(2)}{100}[/tex]
⇒ [tex]S.I = \frac{1320}{100}[/tex]
⇒ S.I = $13.2
Hence, the simple interest of$13.2 is due on loan of $120 for two years with the annual rate of 5.5%.
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I need to calculate the surface area and volume of this figure.
but am not pretty sure
the volume of cone is =1/3 pie r² h
I think this is the formula to calculate it
What’s the complex number in polar form with argument theta between 0 and 2pie?
8+8i
9514 1404 393
Answer:
45. (8√2)∠π/4
46. (7√2)∠3π/4
Step-by-step explanation:
The polar form of a+bi is ...
a +bi ⇔ (√(a²+b²))∠arctan(b/a)
__
45. 8 +8i = (√(8² +8²))∠arctan(8/8) = (8√2)∠π/4
__
46. -7 +7i = (√((-7)² +7²))∠arctan(7/-7) = (7√2)∠3π/4
_____
Additional comment
The arctan function usually returns a value in the range -π/2 to π/2. The quadrant of the desired result can be determined by the signs of the components of the vector. For negative real parts, π needs to be added to the value that is usually returned by the arctan function.
from first-time customers. A random sample of 161 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is between 0.35 and 0.45
Answer:
This probability that the sample proportion is between 0.35 and 0.45 is the p-value of [tex]Z = \frac{0.45 - \mu}{\sqrt{\frac{p(1-p)}{160}}}[/tex] subtracted by the p-value of [tex]Z = \frac{0.35 - \mu}{\sqrt{\frac{p(1-p)}{160}}}[/tex]. These p-values are found looking at the z-table.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Estimate of the proportion:
This is p, and thus, we use [tex]\mu = p[/tex].
Sample of 160
This means that:
[tex]n = 160, s = \sqrt{\frac{p(1-p)}{160}}[/tex]
What is the probability that the sample proportion is between 0.35 and 0.45?
This probability that the sample proportion is between 0.35 and 0.45 is the p-value of [tex]Z = \frac{0.45 - \mu}{\sqrt{\frac{p(1-p)}{160}}}[/tex] subtracted by the p-value of [tex]Z = \frac{0.35 - \mu}{\sqrt{\frac{p(1-p)}{160}}}[/tex]. These p-values are found looking at the z-table.
A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 61 cells.
Find the relative growth rate.
Answer:
the relative growth rate k = ln( 8 )
Step-by-step explanation:
Given the data in the question;
Initial population = 61 cells
which divides into two cells every 20 minutes;
Now.
dy/dt = ky
where y(t) = y(0) [tex]e^{kt[/tex]
y(t) is the population of bacteria
t is time in hours
y(0) is initial population
we know that, Initial population y(0) = 61
time t = 20 min = ( 20 / 60 )hr = 1/3 hr
so, y(1/3) = 2( 61 ) = 122
Now,
y(t) = y(0) [tex]e^{kt[/tex]
y(1/3) = 61 [tex]e^{k\frac{1}{3}[/tex]
122 = 61 [tex]e^{k\frac{1}{3}[/tex]
divide both sides by 122
2 = [tex]e^{k\frac{1}{3}[/tex]
ln(2) = k × 1/3
k = 3ln(2)
k = ln( 2³ )
k = ln( 8 )
Therefore, the relative growth rate k = ln( 8 )
Which graph could represent the equation y=-x^2+4?
Initially 100 milligrams of a radioactive substance was present. After 8 hours the mass had decreased by 2%. If the rate of decay is proportional to the amount of the substance present at time t, determine the half-life of the radioactive substance. (Round your answer to one decimal place.)
For initial 100 milligrams of a radioactive substance was if decreased by 2% in 8 hours, then half-life of the radioactive substance is 108.3 hours.
Rate of change is the change in one variable due to change in other.
Given the following:
Amount of a radioactive substance initially present=100mg
After 8 hours, mass decreased by 2%
Mass after 8 hours= 100-(2% of 100)
=100-(2*100/100)
=100-2
=98
The rate of decay is proportional to the amount of the substance present at time t.
Mathematically,
Let the amount of radioactive substance is A and at time t,
[tex]\dfrac d{dt}A\ \alpha\ A\\\\[/tex]
[tex]\dfrac d{dt}A= kA\\\\\\dA=kAdt[/tex]
On integrating both sides,
[tex]\int \frac {1}{kA}dA=\int dt\\\\[/tex]
[tex]\dfrac {ln A}{k}=t +ln \ c_1\\ln A =kt+k\ ln \ c_1\\[/tex]
On taking antilogarithm both sides,
[tex]e^{ln A} =e^{kt+k\ ln \ c_1\\A=e^{kt}e^{k\ ln \ c_1}\\A=e^{kt}e^{\ ln \ c_1^k}\\A=e^{kt}c_1^k \\[/tex]
Let, [tex]c_1^k=c[/tex]
[tex]A =e^{kt}c[/tex].................................1
At t=0, A=100
Substituting values in 1
[tex]100= e^0c\\c=100[/tex]
At t= 8, A=98
[tex]98=e^{k8}100\\0.98=e^{8k}\\8k=ln0.98[/tex]
k=-0.0064.
To determine the half time of the decay.
At half time A became A/2=50 mg
Substituting in 1.
[tex]50=e^{-0.0064t}100\\ln 0.5=-0.0064t\\t=\frac{ln 0.5}{-0.0064}\\t=108.3042\\t=108.3[/tex]....................................rounded to one decimal place.
Thus, The half-life of the radioactive substance is 108.3 hr.
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Point A’ is the image of Point A when point A is rotated about the origin B. What angle in the counterclockwise direction is A rotated through?
Answer:
90 degrees
Step-by-step explanation:
If 3w +6=21 find the value of w
Answer:
[tex]3w + 6 = 21 \\ 3w = 15 \\ w = 5[/tex]
Hey there!
[tex]\mathsf{3w + 6 = 21}[/tex]
SUBTRACT 6 to BOTH SIDES[tex]\mathsf{3w + 6 - 6 = 21 - 6}[/tex]
CANCEL out: 6 - 6 because that gives you 0 KEEP: 21 - 6 because it helps you solve for w[tex]\mathsf{21 - 6 = \boxed{\bf 15}}[/tex]
NEW EQUATION: [tex]\mathsf{3w = 15}[/tex]DIVIDE 3 to BOTH SIDES[tex]\mathsf{\dfrac{3w}{3}=\dfrac{15}{3}}[/tex]
CANCEL out: [tex]\mathsf{\dfrac{3}{3}}[/tex] because that gives you 1KEEP: [tex]\mathsf{\dfrac{15}{3}}[/tex] because that gives you the value of wNEW EQUATION: [tex]\mathsf{\dfrac{15}{3}=w}[/tex][tex]\mathsf{\dfrac{15}{3}=\boxed{\bf 5}}[/tex]
[tex]\boxed{\boxed{\large\textsf{Therefore, your answer: \huge \bf w = 5}}}\huge\checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
A bookcase contains 2 statistics books and 5 biology books. if 2 books are chosen at random, the chance that both are statistics books is:________
a. 1/21
b. 10/21
c. 11
d. 21/11
Answer:
The chance that both are statistics books is [tex]\frac{1}{21}[/tex]
Step-by-step explanation:
Probability is the greater or lesser possibility of a certain event occurring. In other words, probability establishes a relationship between the number of favorable events and the total number of possible events. Then, the probability of any event A is defined as the quotient between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases. This is called Laplace's Law.
[tex]P(A)=\frac{number of favorable cases}{total number of possible cases}[/tex]
Combination of n elements taken from k to k is called each of the ways of choosing k different elements from the n of the original set. That is, it is called combinations of m elements taken from k to k to all the possible groupings that can be made with the m elements. It is expressed as:
[tex]Cn,k=\frac{n!}{k!*(n-k)!}[/tex]
Remember that the factorial of a positive integer n is defined as the product of all the natural numbers before or equal to it.
A bookcase contains 2 statistics books and 5 biology books. The total number of book is 7.
2 books are chosen at random. The total outcomes can be obtained by selection of two books from seven books which is represented as follows:
[tex]C7,2=\frac{7!}{2!*(7-2)!}=\frac{7!}{2!*5!}=\frac{5040}{2*120} =\frac{5040}{240} =21[/tex]
The selection of two statistics book from two statistics book is represented as follows:
[tex]C2,2=\frac{2!}{2!*(2-2)!}=\frac{2!}{2!*0!}=\frac{2}{2*1} =\frac{2}{2} =1[/tex]
Then, the probability is:
[tex]P(A)=\frac{C2,2}{C7,2}[/tex]
[tex]P(A)=\frac{1}{21}[/tex]
The chance that both are statistics books is [tex]\frac{1}{21}[/tex]
• Javon bought three pencils at a store for $y each. Laila bought four of the same kind
of pencil in another store for $3 more per pencil than Javon did. How much did Javon
pay for his pencils? How much did Laila pay for her four pencils?
Answer:
Javon spent $18 and Laila bought $36
Step-by-step explanation:
Ahm. I don't really know what $y is so i guess it's $6 so
6 x 3
= $18
Laila
6 x 4
= 24 + 3 + 3 + 3 + 3
= 36
$36
THank you ^^
What is the multiplicative inverse of ?
Answer:
MULTIPLICATIVE INVERSE OF X WILL BE 1/X
Step-by-step explanation:
Find the volume of the cubes or rectangular prisms in cubic centimeters.
SS
8
125 cm
126cm
ਹੈ।
135cm
rectangular prism with a length,
width and height of 5 cm. 5 cm.
and 5 cm, respectively
cube with a side length of 5 cm
of a
cube with a side length of 5 cm
rectangular prism with a length,
width and height of 5 cm 5 cm.
and 5 cm, respectively
Answer:
ans : it is order wise
a) 6/125 cm³
b) 8/125 cm³
c) 1/125 cm³
d) 36/125 cm³
Step-by-step explanation:
a)
for rectangular prism = length × width × height
= (1/5) × (2/5) × (3/5)
= 6/125 cm³
b)
for cube = length³
= (2/5)³
= 8/125 cm³
c)
for cube = (1/5)³
= 1/125 cm³
d)
for rectangular prism = (3/5) × (4/5) × (3/5)
= 36/125 cm³
plzz help ill mark u brainliest
A. Angle 4 is congruent to.
b. Angle 5 is congruent to.
c. The sum of angles 1,4 and 5 equals.
d. Therefore the sum of angles of 1, 2, and 3 equals
Answer:
a. angle 4 is congruent to angles 1, 2, 3, 5
b angle 5 is congruent to angles 1, 2, 3, 4
c. the sum of angles 1, 4, and 5 is 180°
d. The sum of angles 1, 2, and 3 is 180 °
Step-by-step explanation:
a. all angles are the same measurement
b. all angles are the same measurement, you know this by measuring
c. they are on a striaght 180 degree line
d. the sum of a triangles angles are always 180 degrees
What is the 5th term in the geometric sequence described by this explicit
formula?
an = 30 • (-2)(n-1)
Answer:
-240
Step-by-step explanation:
n = 5
a₅ = 30* (-2)(5 - 1)
= 30 * (-2)*4
= 30 * (-8)
= - 240
The measures of the angles of triangle ABC are 6x -7; 3x +10; and 10x +25 respectively.Find the measure of each angle of triangle ABCWhat type of triangle is ABC? Explain.
Answer:
41, 34, 105
Step-by-step explanation:
Given that :
Measure of angles :
6x -7; 3x +10; and 10x +25
Recall; sum of angles in a triangle is 180
(6x - 7) + (3x + 10) + (10x + 25) = 180
6x - 7 + 3x + 10 + 10x + 25 = 180
6x + 3x + 10x - 7 + 10 + 25 = 180
19x + 28 = 180
19x = 180 - 28
19x = 152
x = 8
Hence,
6x - 7 = 6(8) - 7 = 41
3x + 10 = 3(8) + 10 = 34
10x + 25 = 10(8) + 25 = 105
3. 72 in. ___ = ft help
Answer:
6 feet
Step-by-step explanation:
Answer:
72in is 6 feet
Step-by-step explanation:
PLEASE HELP ME ANSWER THESE QUESTIONS
Step-by-step explanation:
get a coin and toss it 40 times.....then input your answers....
dont forget to make a prediction about the outcome first
Please assist, I'm really bad with word problems
Answer:
The surface area of the balloon is [tex]S(t) = \frac{100}{49} \pi t^8[/tex]
Step-by-step explanation:
Given;
S(r) = 4πr²
where;
S is the surface area of the balloon
r is the radius of the surface
The radius of the balloon at time "t" is given as;
[tex]r(t)= \frac{5}{7} t^4 \ \ \ t\geq 0[/tex]
The surface area of the balloon as a function of time "t" is calculated as;
[tex]S(t) = 4\pi (\frac{5}{7} t^4)^2\\\\S(t) = 4\pi (\frac{25}{49} t^8)\\\\S(t) = \frac{100}{49} \pi t^8[/tex]
use the cummutative property of addition to write an expression equivalent to 15a+b
Answer:
15a + b = b + 15a
lol is this right?
Step-by-step explanation:
Tori rolls three numbered 1 though 6. She records it weather each cube lands on an even or odd number
Answer:
480 times
Step-by-step explanation:
Given
[tex]n = 50[/tex] ---- total number of rolls
See attachment for complete question
Required
Times OO will appear in a roll of 2000 times
From the attached bar graph,
[tex]n(OO) = 12[/tex]
So, the occurrence of OO in 2000 rolls is:
[tex]OO = \frac{n(OO)}{n} * 2000[/tex]
[tex]OO = \frac{12}{50} * 2000[/tex]
[tex]OO = 0.24 * 2000[/tex]
[tex]OO = 480[/tex]
If a decagon is a regular decagon, then what is the measure of each interior angle?
a. 150°
b. 162°
c. 144°
d. 240°
Answer: the answer is 144 i kinda had the answer already
Step-by-step explanation:
Answer:
c. 144
Step-by-step explanation:
In a regular polygon, each interior angle has the same measure. There is a formula to find the angle given the number of sides. We are looking at a decagon, which has ten sides, so we would plug the value 10 into the following formula:
[tex]\frac{180(n-2)}{n}\\\frac{180(10-2)}{10} \\\frac{180*8}{10} \\18*8\\144[/tex]
This is option c.
I NEED HELP ASAP 30 POINTS - GEOMETRY
2. The general form of a circle is given as x^2 + y^2 + 6x – 14y + 33 = 0
(a) What are the coordinates of the center of the circle? Show all your work.
(b) What is the length of the radius of the circle? Show all your work.
Answer:
Answer:
Center = (-3, 7)
radius = 5
Step-by-step explanation:
x² + y² + 6x – 14y + 33 = 0
Put the equation in standard form:
(x - h)² + (y - k)² = r²
(h, k) is the center
r is the radius
---------------------------
Regroup
x² + 6x + y² - 14y = -33
Complete the square for x
(x + 3)² + (y - 7)² = -33 + 3² + (-7)²
(x + 3)² + (y - 7)² = 25
Center = (h, k) = (-3, 7)
radius = √25 = 5
Which pair of angles are complementary?
Answer:
Two Angles are Complementary when they add up to 90 degrees (a Right Angle). They don't have to be next to each other, just so long as the total is 90 degrees. Examples: 60° and 30° are complementary angles.
Answer:
Step-by-step explanation:
those two angles which gives 90 degree when added are complementary angles.
A box plot is shown. The left-most point on the plot is 20 and the right-most point is 95. The box is labeled 35 on the left edge and 60 on the right edge. A vertical line is drawn inside the rectangle at the point 55.
Part A: List two pieces of information that are provided by the graph and one piece of information that is not provided by the graph. (4 points)
Part B: Calculate the interquartile range of the data, and explain in a sentence or two what it represents. (4 points)
Part C: Explain what affect, if any, there will be if an outlier is present. (2 points)
PLEASE ONLY ANSWER IF YOU KNOW WHAT IT IS!!
"The box plot tells us about the lower limit, first quartile, median, third quartile, and upper limit.
Step-by-step explanation:
Box plot:
It displays the five-number summary of a set of data. The five-number summary is the lower limit, first quartile, median, third quartile, and upper limit. We draw a box in a box plot from the first quartile to the third quartile. A vertical line goes through the box which represents the median. Anything that lies beyond the upper limit or the lower limit is know as an outlier.
From the information given, we can say that:
The left-most point on the plot is 20 and the right-most point is 95 which means 20 and 95 are the lower and upper limit respectively. The box is labeled 35 on the left edge and 60 on the right edge which means 35 is the first quartile and 60 is the the third quartile. A vertical line is drawn inside the rectangle at the point 55 which means 55 is the median of given data. We cannot know about the mean of data with the given information."
(this is kind of an answer, I hope it's helpful)
The other prson is right, give them brainliest!
STEM:
If you can rewrite a quadratic equation as a product of factors that equals zero, you
can solve the equation. To solve equations in this manner, you must use all your
factoring skills.
Example:
What are the solutions of the equation x2– x = 20?
First rewrite the equation so that one side equals zero.
x2– x = 20
x2 – x – 20 = 20 – 20
x2 – x – 20 = 0
Subtract 20 from each side.
Simplify.
Now, factor to rewrite the equation as a product of factors equal to zero. Find two
integers whose product is –20 and whose sum is –1. The product of 4 and –5 is
–20, and the sum of 4 and –5 is –1.
x + 4 = 0
x + 4 – 4 = 0 – 4
x = –4
x2 – x – 20 = 0
(x + 4)(x – 5) = 0
or
or
or
x – 5 = 0
x – 5 +5 = 0 +5
x = 5
The solutions are –4 and 5.
These "solutions" tell us where our quadratic function passess through the x-axis (ie this tells us the "roots" aka "x -intercepts" aka "zeros" aka "solutions" aka "zeros" are)
Question:
In the graph provided in the example, what do the coordinates (-4,0) and (5,0) represent?
A
The y- intercept of the function (ie where the function passes through the y-axis)
B
The x-intercept of the function (ie where the function passes through the x-axis)
C
The vertex of the function
D
none of the above
E
the zeros of the quadratic function
F
the roots of the quadratic function
9514 1404 393
Answer:
A, E, F
Step-by-step explanation:
Every point on the graph has coordinates (x, f(x)). This means a point such as (-4, 0) or (5, 0) is a point on the x-axis where f(x) = 0. It is all of ...
an x-intercepta root of the functiona zero of the functionThese terms are used essentially interchangeably.
Decide whether the equation describes a function.
y = - 4x-1
Does the equation describe a function?
Yes
Νο.
Answer:
[tex]{ \tt{yes \: it \: describes \: a \: functional \: equation \: of \: a \: line}}[/tex]
Write the equation of a vertical line that passes through the point (-5,0)
Answer:
x=-5
Step-by-step explanation:
A vertical line is a line that goes up and down. It has a constant x value
Since the x value is -5
x=-5
Pls helllllpppppp!!! I don’t want anymore lectures from my parents and I don’t want to be the bad guy anymore. I need my grades up so pls no links or fake answers.
Your mom suggested ten different choices for you to eat for dinner over the next week. How many different ways can you choose your dinner?
A. 120
B. 240
C. 720
D. 960
Answer: I think the answer is 120
Step-by-step explanation:
I'm not sure tho
Triangles RST and MNP are congruent. Name the congruent sides and the congruent angles.
Answer:
angles:r=m
s=m
t=p
sides:rs=mn
rt=mp
st=pn
Alexia veut préparer un cocktail original
Answer:
????????????????????
