The interest rate for a $6000 deposit accumulating to $6957, compounded annually for 6 years is r=2.49%.
What is meant by interest rate?The interest rate is the amount charged by the lender to the borrower over and above the principal amount. In terms of the receiver, a person who deposits money in any bank or financial institution obtains additional revenue due to the time value of money, which is referred to as interest received by the depositor.
Here's a simple interest formula: Interest = P x R x T, P = Principal Amount (the beginning balance).
Given, Amount=6957, P=6000, t=6 years
A=P[tex](1+(r/n)^{nt}[/tex]
6957=6000(1+(r/1))[tex](1+(r/1))^{6}[/tex]
[tex](1+(r/1))^{6}[/tex]=6957/6000
=1.1595
ln[tex](1+(r/1))^{6}[/tex]=ln(1.1595)
6(1+(r/1))=ln(1.1595)
(1+(r/1))=ln(1.1595)/6=0.0246
(1+(r/1))=[tex]e^{0.0246}[/tex]
1+r=1.02490508
r=0.02490508
r=2.49%
The interest rate for a $6000 deposit accumulating to $6957, compounded annually for 6 years is r=2.49%.
To know more about interest rate, visit:
https://brainly.com/question/13324776
#SPJ1
Factor completely ^2-7r-18
John's bank account was overdrawn. The status of his account was -107. He did not realize the problem and wrote another check for $43. The bank charged him a $22 fee for being overdrawn.
Answer: -$155
Step-by-step explanation:
Using this formula
New status=(-Account status-Cheque amount)-Bank charges
Let plug in the formula
New status= (-$112-$22)-$21-
New status=-$134-$21
New status=-$155
Inconclusion The new status of John's account at this point is -$155
Learn more here:
brainly.com/question/13147505
A medical researcher collects health data on many women in each of several small countries. One of the variables
measured for each woman in the study is her weight in pounds. The following list gives the five-number:
summary for the weights of adult women in one of the countries.
Country A:
92, 110, 120, 160, 240
About what percent of Country A women weigh between 110 and 240 pounds? Show your work.
(a) 50%
(b) 65%
(c) 75%
(d) 85%
(e) 95%
Option (c) 75% of Country A women weigh between 110 and 240 pounds.
What is the five-number summary?
When conducting descriptive analyses or conducting an initial analysis of a sizable data set, a five-number summary is particularly helpful. The maximum and minimum values in the data set, the lower and upper quartiles, and the median make up a summary's five values.
Given, the five-number summary of Country A:
92, 110, 120, 160, 240
Then, we get
Minimum value = 92, First quartile = 110, Median = 120, Third quartile=160,
Maximum value = 240
Between 110 and 240 pounds, data lies from the First quartile to Maximum value which represents 75% of the data.
Hence, Option (c) 75% of Country A women weigh between 110 and 240 pounds.
To learn more about the five-number summary
https://brainly.com/question/17110151
#SPJ1
Could someone please help me with this?
Answer: yes, 1/3, 1/3x
Step-by-step explanation:
Does x vary directly with y?
This basically means is this a linear function and the answer is yes it is.
What is the constant of variation?
The constant of variation is 1/3 because you have to multiply each x value by 1/3 to get the y value
What is the function rule?
y = 1/3x
Help please and asap thank you asap !!!!!!
Answer:
F(x) = m1/5
Step-by-step explanation:
. Graph the function f(x) = x
^2 + 7x + 10 on the coordinate plane.
The graph of the function f(x) = x² + 7x + 10 is attached.
What is the general equation of a parabola?A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line. The fixed point is called the focus of the parabola, and the fixed line is called the directrix. The general equation of a parabola is -
y = a(x - h)² + k
We have the following equation of a quadratic equation representing parabola as -
f(x) = x² + 7x + 10
Refer to the graph of the function f(x) attached. It can be seen that it is a parabola opening upwards.
Therefore, the graph of the function f(x) attached.
To solve more questions on Parabolas, visit the link below -
brainly.com/question/20333425
#SPJ1
If a six-sided number cube is rolled 5 times, what is the probability of getting at least one multiple of 3?
The probability of getting at least one multiple of 3 when a six-sided number cube is rolled 5 times is 1/7776 or 0.01%.
What is probability?Probability shows the likelihood of an event happening. it can be calculated by dividing the number of outcomes of an event by the total number of possible outcomes or sample space. Probability is equal to '1' when the event is certain to occur. i.e P =1.
Probability of getting at least one multiple of 3 = 1/6.
Probability of getting at least one multiple of 3 five times = probability of getting at least one multiple of 3 first time×probability of getting at least one multiple of 3-second time×probability of getting at least one multiple of 3 third time ×probability of getting at least one multiple of 3 fourth time ×probability of getting at least one multiple of 3 fifths time.
Probability of getting at least one multiple of 3 five times
= (1/6) × (1/6) × (1/6) × (1/6) × (1/6)
= 1/7776.
Learn more about probability on
brainly.com/question/17084679
#SPJ1
Jenny had 947 marbles.
She gave 515 of these marbles away.
How many marbles does she have left?
Answer: 432
Step-by-step explanation: 947- 515 = 432.
My subtracting 515 from 947, the answer becomes 432. You can double check this statement by adding 515 and 432 together.
If $8000 is invested at an annual interest rate of 5% and compounded annually, what is the balance after 4 years?
Answer: 7 years
Step-by-step explanation:
We make the assumption that 8000 is 100% since it is our output value.
Step 2: We next represent the value we seek with $x$.
Step 3: From step 1, it follows that $10\%=8000$.
Step 4: In the same vein, 100%=8000$.
So divide that by 5% 0.05%
Then multiply it by 5 0.0025%
Then convert it into money 26$
The perimeter of a rectangle is 34 centimeters. The length is two more than twice the width. Find the length and the width of the rectangle.
The length of a rectangle is 12 units and width is 5 units.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
To determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given that the Perimeter of a rectangle = 34 cm.
and, length is two more than twice the width.
Thus the width be x.
So, the length = 2x + 2
So,
Perimeter of rectangle = 2 ( l +w )
34 = 2( x+ 2x+ 2)
17 = 3x +2
3x = 15
x= 5
2(5)+2 = 12
So, The length is 12 units and width is 5 units.
Learn more about Algebra here:
brainly.com/question/24875240
#SPJ1
PLEASE HELP!
Which translation rule matches the transformation for congruent triangles?
The translation applied to the triangle is:
T(x, y) → (x +4, y - 5)
Sp the correct option is the first one.
Which is the rule of the translation from GHI to G''H''I''?To analyze the translation we only need to compare the coordinates of one of the vertices.
Let's see the vertex H.
The coordinates of H are (-4, 1)
The coordinates of H'' are (0, -4)
Then the translation is defined by the difference between these coordinates:
(0, -4) - (-4, -1) = (4, -5)
Then the translation here is:
T(x, y) → (x +4, y - 5)
So the correct option is the first one.
Learn more about translations:
https://brainly.com/question/24850937
#SPJ1
As a construction worker, you are building a cylindrical grain silo with a radius of 10 meters and a volume of 6,280 cubic meters.
Which formula will determine the height of the silo? Rounded to the nearest whole number of meters, what is the height of the silo?
, 6 meters
, 14 meters
, 20 meters
, 25 meters
, 80 meters
Answer:
[tex]h=\frac{V}{\pi r^{2} }[/tex], 20 meters
Step-by-step explanation:
The formula for the volume of the silo is: [tex]V=\pi r^{2} h[/tex]
You are given:
Volume= 6,280 cubic meters
Radius= 10 meters
Therefore, you can solve for the height by getting h on it's own side.
The formula for the height of the silo is given by: [tex]h=\frac{V}{\pi r^{2} }[/tex]
Now solve using the given values: [tex]h=\frac{6,280}{\pi (10)^{2} }[/tex]
The height of the silo = 20 meters
ASAP PLEASE FOR POINTS
A regular polygon is shown, with one of its angle measures labeled a
If m
z=15
z=20
Z=23
Z=41
Answer:
Step-by-step explanation:
(-6) • (-2) what is it the
[tex]\fbox{12}[/tex]
When multiplying two negative numbers, the answer will always be positive.
[tex]-6\times-2[/tex]
[tex]=12[/tex]
What is the average rate of change of this function on the interval from x = 1 to x = 3? f(x)=10(2)x Enter your answer in the box.
Answer:
30
Step-by-step explanation:
The way to figure out the average rate of change is to divide the change in f(x) and divide that by the change in x. A formula for this is [tex]\frac{f(x_{1})-f(x_{2})}{x_{1}-x_{2}}[/tex]
1.) By this definition, we need to figure out our x1 and x2. We can say the x1 = 3 and x2 = 1
2.) Next, we plug it into the formula. We will get [tex]\frac{f(3)-f(1)}{3-1}[/tex].
3.) If we simplify, we will get 10(2)^3 - 10*2 divided by 2, which is equal to 10*4 - 10 = 30.
Which rectangle has side lengths of 5 units and 6 units?
The rectangle that has side lengths of 5 units and 6 units is (b) the rectangle that has a perimeter of 22 units
How to determine the rectangle?The complete question is added at the end of this solution
From the complete question, we have the following parameters that can be used in our computation:
Side lengths = 5 units and 6 units
These side lengths can be represented as
Length = 5 units
Width = 6 units
The area of a rectangle is calculated as
Area = Length * Width
Substitute the known values in the above equation, so, we have the following representation
Area = 5 units * 6 units
Area = 30 square units
The perimeter of a rectangle is calculated as
Perimeter = 2 * (Length + Width)
Substitute the known values in the above equation, so, we have the following representation
Perimeter = 2 * (5 units + 6 units)
Perimeter = 22 units
Comparing the above to the options, we have
(b) The rectangle with a perimeter of 22 units
Hence, the true statement is (b)
Read more about rectangles at
https://brainly.com/question/25292087
#SPJ1
Possible question
Which rectangle has side lengths of 5 units and 6 units?
(a) The rectangle with an area of 22 square units
(b) The rectangle with a perimeter of 22 units
(c) The rectangle with a perimeter of 22 square units
(d) The rectangle with an area of 30 units
For the functions f(x) = 2x-5 and g(x) = 3x²-x, find (fog)(x) and (gof)(x).
The fog(x) of the function will be 6x² -2x - 5 and gof(x) of the function will be 12x² + 62x - 80.
What is the domain of a function?
The collection of values that can be plugged into a function's domain is called its parameters. The x values for a function like f(x) are contained in this collection (x). The collection of numbers that the operator assumes is known as its range.
As per the given information in the question,
f(x) = 2x - 5 and,
g(x) = 3x² - x
fog(x) = 2x - 5 and,
gof(x) = 2x - 5
fog(x) = f(g(x))
= f (3x² - x) = 2(3x² - x) -5
= 6x² -2x - 5
gof(x) = g(f(x))
= g (2x - 5) = 3(2x - 5)² + 2x - 5
= 12x² - 75 + 60x + 2x -5
12x² + 62x - 80.
To know more about Domain:
https://brainly.com/question/28135761
#SPJ1
If h(x)=5x-6 which expression is equivalent to (h+h)(2)?
A 5(2+2)-6
B 5[5(2)-6]-6
C 52-6+52-6
D 5(2)-6+5(2)-6
The equivalent of (h+h)(2) of the function h(x) = 5x - 6 is 5[5(2) - 6] -6 which is option B
What is a function?
A technical definition of a function is: a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
This means that if the object x is in the set of inputs (called the domain) then a function f will map the object x to exactly one object f(x) in the set of possible outputs (called the codomain).
h(x) = 5x - 6
(h + h)(x) = h(x) in x. This means put the function in h(x)
so x = 5x - 6
so (h + h)(x) = 5(5x-6) -6
if x = 2,
we have (h + h)(2) = 5[5(2) -6] -6
In conclusion the expression 5[5(2) -6] -6 is equivalent to (h+h)(2)
Learn more about function: https://brainly.com/question/10439235
#SPJ1
Cari is searching online for airline tickets. Two weeks ago, the cost to fly from boston to denver was $220. Now the cost is $295. What is the percent increase? What would be the percent increase if the airline charges an additional $50 baggage fee with the new ticket price?
The percent increase with the additional baggage fee for airline would be $125 / $220 x 100% = 56.82%.
What is meant by the term percentage?A number can be expressed as a fraction of 100 using a percentage. It may be computed by dividing the number by the total and multiplying by 100. It is commonly represented by the sign "%". The percentage of men, for instance, would be 25/100 x 100, or 25%, if there were 100 persons in all.
In a variety of areas, including statistics, finance, and education, percentages are often employed. For instance, in finance, percentage increase in stock prices are used to gauge a market's or company's success. In education, grades are frequently given as percentages to represent class marks.
How to solve?
The increase in the cost of the ticket is $295 - $220 = $75
The percent increase is $75 / $220 x 100% = 34.09%.
If the airline charges an additional $50 baggage fee, the new ticket price would be $295 + $50 = $345.
The increase in the cost of the ticket with the additional baggage fee would be $345 - $220 = $125.
The percent increase with the additional baggage fee would be $125 / $220 x 100% = 56.82%.
To learn more about percentage, visit:
https://brainly.com/question/14979505
#SPJ1
Given f(x) =(4-x)², what is the value of f(16)?
Answer:
144
Step-by-step explanation:
Answer:48
Step-by-step explanation:
Wherever you see an x on the right, you put a 16. That's what f(16) means.
f(16) = 1/3 (4 - 16)^2
f(16) = 1/3 (- 12)^2
f(16) = 1/3 (144)
f(16) = 48
An urn contains 100 marbles. Fifty are purple, ten are green,
fifteen are red, and twenty-five are orange. Two marbles are drawn
at random one after another without replacement. Calculate each probability.
The probability of picking a purple and green marbles is 0.05.
What is a probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.
Number of purple marble = 50
Number of green marbles = 10
Total number of marbles = 100
The probability of picking a purple and green marbles will be:
= 50/100 × 10/99
= 0.05
Learn more about probability on:
brainly.com/question/24756209
#SPJ1
Complete question
A urn contains 100 marbles. Fifty are purple, ten are green, fifteen are red, and twenty-five are orange. Two marbles are drawn at random one after another without replacement. Calculate the probability of picking a purple and green marbles
What is the Minimum value of k=
Answer:
k = -3
Step-by-step explanation:
Lines in the form y=k are horizontal. The lowest point on the parabola has a y-value of -3. That is the value where y=-3 will intersect the parabola at exactly one point. Every k value above this will have 2 points of intersection.
Which of the following points lie on a line that passes through the origin with a slope of −25? Select all that apply. Multiple select question. cross out A) (0, 0) cross out B) (1, −25) cross out C) (−2, 5) cross out D) (−1, 25) cross out E) (4, 10) cross out F) (−5, 2)
The points that will lie on the line will be (0, 0) , (1, - 25) , (- 1, 25).
What is the general equation of a straight line?The general equation of a straight line is : y = mx + c.
[m] is called slope and it tells the unit rate of change in [y] with respect to [x].
[c] is called the [y] - intercept.
We have some points that lie on a line that passes through the origin with a slope of −25.
The equation of a straight line that passes through the origin and has slope of -25 will be -
y = - 25x
The points that will lie on the line will be -
(0, 0) , (1, - 25) , (- 1, 25)
Therefore, the points that will lie on the line will be (0, 0) , (1, - 25) , (- 1, 25).
To solve more questions on Equations, Equation Modelling and Expressions visit the link below -
brainly.com/question/14441381
#SPJ1
What is the probability of drawing an odd number or a heart
out of a deck of cards?
Answer:100/10000000000
Step-by-step explanation:qazwsxeedcrfvtgbyhn
"Let U={b, c, d, e, f, g, h} and A={b, f, g, h}. Use the roster method to write the set A'
A'= {____ }
(Use a comma to separate answers as needed.)"
If U = {b, c, d, e, f, g, h} and A = {b, f, g, h}, using the roster method to write the set A' which is the set complement of A gives; A' = {c, d, e}
How to find the complement of the set?Sets are defined as groups of clearly specified components. The number of items that exist in a finite set is denoted by a curly bracket.
We are given;
Universal Set U = {b, c, d, e, f, g, h}
Subset A = {b, f, g, h}.
The roster method to write the set A' which is the complement of A will be expressed as;
A' = U - A
Thus;
A' = {b, c, d, e, f, g, h} - {b, f, g, h}
A' = {c, d, e}
The roster method to write the set A' will be {c, d, e}.
Read more about complement of set at; https://brainly.com/question/17513609
#SPJ1
Which equation represents a line passing through the point (8, 33) with a slope of 3?
Answer:
y = 3x + 9
Step-by-step explanation:
y = 3x + b
33 = 3(8) + b
33 = 24 + b
b = 9
y = 3x + 9
Could you please give me brainliest for this? Thank you!
what are numbers with exactly three prime factors?
Answer:30
Step-by-step explanation:
30 is the smallest number that has three different prime factors.
During WW! mortars were fired from trenches 3 feet down The mortars had a velocity of 150 ft/s. Determine how long it will take for the mortar shell to strike its target?
In 0.02 seconds, the mortar shell will make contact with the target.
How to determine the time it will take the mortar shell to strike the targetThe formula for velocity, which is equal to distance / time, is used to calculate how long it will take to hit the target.
In the problem, the distance is 3 feet, and the velocity is given to be 150ft/s
therefore
150 = 3 / time
time = 3 / 150
time = 0.02 seconds
Learn more on velocity at:
https://brainly.com/question/25749514
#SPJ1
help pls asap The polygon circumscribes a circle. What is the perimeter of the polygon?
Applying the two-tangent theorem, the perimeter of the polygon = 70 cm.
What is the Perimeter of a Polygon?To find the perimeter of a polygon, sum all the side lengths of the polygon all together.
What is the Two-tangent Theorem?If two tangent segment of a circle are drawn to meet at a point outside the circle, the two-tangent theorem says they are congruent together, that is, they have equal length.
Applying the two-tangent theorem, the following side lengths that are missing as labelled in the diagram attached below are:
a = 13 cm
b = 9 cm
c = 5 cm
d = 8 cm
Therefore:
Perimeter of the polygon = 13 + a + b + 9 + 5 + c + d + 8
Plug in the values
Perimeter of the polygon = 13 + 13 + 9 + 9 + 5 + 5 + 8 + 8 = 70 cm.
Learn more about the perimeter of polygon on:
https://brainly.com/question/3310006
#SPJ1
20 points and brainliest
Answer:
A,B,C
Step-by-step explanation:
the number in x has to be a different number it can't be the same
example:
2x+3=5x+79
wrong way:
5x+3=5x+79
that equals no solution
hope this helps