You invest $300 at 4% interest, compounded every year. What will your balance be after 5 years? (Remember, the formula is A = P(1 + r)t. ) A. $365. 00 B. $350. 96 C. $364. 65 D. $382. 88
Therefore , the solution of the given problem of interest rate comes out to be the amount after 5 years is A ≈ 364.996.
Define interest rate.With the help of an interest rate, you can determine how much borrowing will cost you and how much saving will yield. As a result, the interest rate is the cost of borrowing money and, if you're a borrower, it's expressed as a percentage of the total loan amount. An amount, expressed as a percentage of the loan amount, that a borrower is required to pay to a lender as interest during the term of a loan.
Here,
Given : Principal amount : $300
rate of interest : 4%
and time =5 years
Thus , to find the amount after 5 years as compounded
We use , the formula:
=> A = P
=> A =
=> A =
=> A ≈ 364.996
Therefore , the solution of the given problem of percentage comes out to be the amount after 5 years is A ≈ 364.996.
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The amount after 5 years with compound interest rate is option(A) = $365. 00.
What is called interest rate?The amount a lender charges a borrower is called an interest rate, and it is expressed as a percentage of the principal, or the loaned amount. Typically, a loan's interest rate is expressed as an annual percentage rate, or APR (APR).
A savings account or certificate of deposit earnings at a bank or credit union may also be subject to an interest rate (CD). The interest received on these deposit accounts is measured in annual percentage yields (APY).
Given : Principal amount : $300
rate of interest : 4% (compounded yearly)
time =5 years
Thus , to find the amount after 5 years as compounded we use , the formula:
=> A = P(1 + r/100)^t.
=> A = $300 (1 +4/100)^5
=> A = $300 (104/100)^5
=> A = $300 (1.04)^5
=> A = $300 * 1.2167
=> A = $365.00
The amount after 5 years with compound interest rate is option(A) = $365. 00.
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The brain volumes ?( cm cubed cm3?) of 20 brains have a mean of 1083. 9 1083. 9 cm cubed cm3 and a standard deviation of 122. 2 122. 2 cm cubed cm3. Use the given standard deviation and the range rule of thumb to identify the limits separating values that are significantly low or significantly high. For such? data, would a brain volume of 1348. 3 1348. 3 cm cubed cm3 be significantly? high?
Therefore , the solution of standard deviation is because the value of 1452.2 cm3 does not fall between the range of 917.4 cm3 and 1422.2 cm3.
what is the standard deviation?Standard deviation, often known as variance in a set of data, is a statistical measure of variation. A low standard deviation indicates that the values are more likely to be near the mean of the collection, whereas a high standard deviation indicates that the values are widely distributed. How far the data depart from the mean is expressed by the standard deviation, abbreviated as.
Here,
Considering the details here,
The average brain volume is 1169.8 cm3, while the standard deviation is 126.2 cm3.
The much lower results are u-2 = 11169.8-2(126.2) => 917.4.
Reason: According to the range rule of thumb, the required incredibly low values are 91.7 cm3 or less.
Hint: Use the algorithm to identify values that are at least considerably high.
Step: 2
Considering the data supplied,
The average brain volume is 1169.8 cm3, while the standard deviation is 126.2 cm3.
Significantly higher values include,
u-2α = 11169.8+ 2(126.2)
=> 1422.2
Justification: According to the range rule of thumb, the necessary significantly high values must be 1422.2 cm3 or higher.
Hint: To determine whether the value 1452.2 cm3 is very high, use the findings of steps (1) and (2).
Step: 3
Using step 1 and step (4),
917.4 is among the significantly low numbers or less.
The significantly high values are 1422.2 or higher.
Yes, 1452.2 cm3 is a noticeably high value.
The apt response is choice (B).
Reason: The value is much higher than expected based on the range rule of thumb because the value of 1452.2 cm3 does not fall between the range of 917.4 cm3 and 1422.2 cm3.
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What is the product of 3p and 4p² 5p 7?
The product of 3p, 4p² and 5p 7 is 120p⁹.
What is product?Product is an item or thing that is created or produced by a business. It can refer to both physical and intangible items, such as machines, food, software, intellectual property, or services. The concept of a product is used in many different industries, including manufacturing, retail, technology, and finance. Products are typically sold in exchange for money, but can also be given away or traded. Products are an essential part of any business, as they are what generate income for a company.
This can be calculated by multiplying 3p (3 x p) with 4p² (4 x p²) and 5p 7 (5 x p x 7). The result of this multiplication is 120p⁹ (3 x 4 x 5 x p x p² x 7).
To understand this calculation better, we can break it down into its component parts.
The 3p component is 3 x p, which gives us 3p. The 4p² component is 4 x p², which gives us 4p². The 5p 7 component is 5 x p x 7, which gives us 5p 7. When these three components are multiplied together we get 3 x 4 x 5 x p x p² x 7,which is equivalent to 120p⁹.
In conclusion, the product of 3p, 4p² and 5p 7 is 120p⁹.
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A family visits a car show to research information on vehicles they might consider purchasing. Brochures for each vehicle provide helpful information for the vehicle. Which of the following is an example of a continuous quantitative variable that might be included in the brochure?
number of seats
type of transmission
presence of a sunroof
fuel efficiency (in mpg)
answer is fuel efficiency
Since the family visits a car show to research information on vehicles they might consider purchasing. The option that is an example of a continuous quantitative variable that might be included in the brochure is option D: fuel efficiency (in mpg).
What is continuous quantitative variable?A continuous quantitative variable is a type of variable that can take on any value within a certain range, such as fuel efficiency which can take on any value between a certain range of miles per gallon (mpg). In contrast, a categorical variable can only take on a discrete set of values.
"Number of seats" is also a continuous quantitative variable, but it is a bit different in the sense that it only can take on a certain values, for example the possible values for number of seats in a car can only be 2,4,5,6, etc.
Type of transmission is not a continuous quantitative variable, but it's a categorical variable, it can only take certain values such as Automatic, manual, etc.
Note also that presence of a sunroof also not a continuous quantitative variable, but it's a binary categorical variable which has only two possible values: true (presence) and false (absence)
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Which functions have an axis of symmetry of x = –2? Check all that apply.
f(x) = x2 + 4x + 3
f(x) = x2 – 4x – 5
f(x) = x2 + 6x + 2
f(x) = –2x2 – 8x + 1
f(x) = –2x2 + 8x – 2
The quadratic functions that have an axis of symmetry at x = -2 are given as follows:
f(x) = x² + 4x + 3.f(x) = -2x² - 8x + 1.How to obtain the axis of symmetry of a quadratic function?The standard definition of a quadratic function is given by the rule presented as follows:
y = ax² + bx + c, in which a is different of zero.
The axis of symmetry is given by the x-coordinate of the vertex, hence it's equation is defined as follows:
x = -b/2a.
Meaning that the correct options are given by the first and by the fourth options in this problem.
For the first function, we have that:
a = 1, b = 4.
Hence the axis of symmetry is obtained as follows:
x = -4/2 = -2.
For the fourth function, we have that:
a = -2, b = -8.
Hence:
x = -8/4 = -2.
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The town librarian bought a combination of new-release movies on DVD for $20 and classic movies on DVD for $8. Let
x represent the number of new releases, and let y represent the number of classics. If the librarian had a budget of
$500 and wanteho purchase as many DVDs as possible, which values of x and y could represent the number of new
release and classie movies bought?
O x= 8, y = 45
O x= 10, y = 22
O x = 16. Y = 22
Ox= 18, y=18
Mark this and return
Save and Exit
Next
Submit
The Correct answer is option (C) x = 16. Y = 22 . number of new-release movies on DVD is 16 and the number of classic movies on DVD is 22 .
What is linear equation?An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.
Given,
To find the values of X and Y,
Let x = number of new releases
Let y = number of classics.
The equation to solve the question is ,
20x + 8y = 500
When x= 16 and y = 22
= 20x + 8y
= 20(16) + 8(22)
= 320 + 176
= 496
Therefore, the number of new-release movies on DVD is 16 and the number of classic movies on DVD is x= 16, y = 22
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wacky wizards offers beginner and advanced magic classes. The beginner class costs 6 more than half the cost of the advanced class.Last week they taught 7 beginner classes and 11 advanced classes and earned $390. Write a system that represents the cost of the beginner class, b and the advanced class, a. HELP!!!!!
The system represents the cost of the beginner class will be $18 and the advanced class will be $24.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Both basic and expert magic lessons are available at Wacky Wizards. More than half as much is spent on the introductory class as there is on the advanced level. They made $390 last week by instructing 7 basic lessons and 11 advanced classes.
Let 'x' be the cost of beginner classes and 'y' be the cost of advanced classes. Then the equations are given as,
x = y / 2 + 6
y = 2x - 12 ...1
7x + 11y = 390 ...2
From equations 1 and 2, then we have
7x + 11(2x - 12) = 390
7x + 22x - 132 = 390
29x = 522
x = 18
Then the value of the variable 'y' is calculated as,
y = 2(18) - 12
y = 36 - 12
y = 24
The system represents the cost of the beginner class will be $18 and the advanced class will be $24.
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What is y=-6x+2 in standard form
In describing the cost equation, Y = a + bX, "a" is:
- A) The dependent variable cost.
- B) The independent variable the level of activity.
- C) The total fixed cost.
- D) The variable cost per unit of activity.
Answer:
C) The total fixed cost.
Sara put her dog on a diet and kept track of his weight. At the end of 4 weeks,
she recorded her dog's weight change as -3 1/2 pounds. She noticed her dog lost
the same amount of weight each week. What is the dog's weight change each
week of the diet?
Answer:
Weight change per week = -0.875 or -7/8
Step-by-step explanation:
Sara recorded her dog's weight change as -3.5 pounds after 4 weeks of dieting. We know the weight loss is consistent each week, so we need to find out how much the dog loses in one week.
To find out the weight change per week, we can use the formula:
Weight change per week = Total weight change / Total number of weeks
Plugging in the known values:
Weight change per week = -3.5 / 4
Weight change per week = -0.875
The dog loses 0.875 pounds each week.
or -0.875 pounds is the weekly weight change of the dog during the dieting period.
The number of rats living in an abandoned building increases each year. The total number of rats can be described by this sequence: 2, 6, 18, 54, 162, ...
What is the explicit formula?
What is the recursive formula?
Please help with the recursive formula the most if you can!
Answer: The explicit formula for this sequence is given by the expression a_n = 3^n, where n is the position in the sequence (starting from n=1 for the first term).
The recursive formula for this sequence is given by the expression a_n = 3a_(n-1), where n is the position in the sequence (starting from n=1 for the first term) and a_(n-1) is the previous term in the sequence.
Here's how you can use the recursive formula to find the terms of the sequence:
a_1 = 2
a_2 = 3a_1 = 3 * 2 = 6
a_3 = 3a_2 = 3 * 6 = 18
a_4 = 3a_3 = 3 * 18 = 54
a_5 = 3a_4 = 3 * 54 = 162
and so on.
To find the explicit formula, you can try to find a pattern in the terms of the sequence. For example, you might notice that each term is simply the previous term multiplied by 3. This pattern can be expressed using the recursive formula a_n = 3a_(n-1). To find the explicit formula, you can then solve for a_n in terms of n:
a_n = 3a_(n-1)
a_n / 3 = a_(n-1)
a_n / 3 = (3a_(n-2)) / 3
a_n / 3 = 3^(n-2)
a_n = 3^n
Therefore, the explicit formula for this sequence is a_n = 3^n.
Step-by-step explanation:
The sum of the digits of a two-digit number is 12. The number formed by reversing the digits is 54 more than the original number. What is the original number?
48
39
57
Answer:
39
Step-by-step explanation:
A commuter wants to determine the average price of gas in the area. Which is the best method of collecting a population sample so that the commuter can answer this question? Responses: A. Check gas prices at several gas stations near the commuter’s house. B. Find the gas prices over the past several years at a single particular gas station in the area. C. Look up a number of randomly selected gas stations in the area to find out gas prices. D. Survey friends on social media to see how much people are paying for gas.
The best method of collecting a population sample so that the commuter can answer this question is C. Look up a number of randomly selected gas stations in the area to find out gas prices.
What is the population?The entire group about which you want to draw conclusions is referred to as a population. The particular group from which you will gather data is known as a sample. The sample size is always smaller than the total population size.
A sample is characterized as a more manageable and compact version of a larger group. a smaller population that possesses the traits of a larger population. When the population size is too large to include all participants or observations in the test, a sample is used in statistical analysis.
This method would be the most representative of the entire population of gas stations in the area, and therefore the most likely to produce an accurate average price.
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Plot all of the points of the reflected figure.
You may click a plotted point to delete it.
y
-10 9 8 7 6 5
-4 3
-2
-1
10
9
8
7
6
сл
2
↓
$
co
4
-5
ન
19
N
3
4
5
6
7
8 9
10
-x
Just re dot the points like mirror it on where ever on the graph
How do you plot a reflection on a point?Use the same x-coordinate and the y-opposite coordinate's to reflect a point on the x-axis. Use the same y-coordinate and the x-opposite coordinate's to reflect a point on the y-axis.
A point can be reflected in the x-axis, y-axis, or both axes.
Due to identical x-coordinates and opposing y-coordinates, the red spots on the x-axis are mirror reflections of one another. Thus, in opposing directions and 3 units away from the x-axis, are the red spots. A reflection in the x-axis is shown by the red spots.
Due to the identical y-coordinates and opposing x-coordinates, the blue spots on the y-axis are mirror reflections of one another. the blue points are thus
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find the output, g, when the input, r is 3
g= -5 + 13
The output of function g(r) = -5x + 13 when r is 3 is -2.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
g(r) = -5r + 13
Input r = 3
g(3)
= -5 x 3 + 13
= -15 + 13
= - 2
Thus,
The output is -2.
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Finding the Probability of Simple Events
Answer:
th chicken
Step-by-step explanation:
help need answered today PLEASE
first answer thats correct will get brainly crown
Answer:
2/3
Step-by-step explanation:
Slope = rise / run = 2 / 3
Because points A, B, C, and D are collinear (meaning on the same line), the slope for line segment AB is the same as the slope for segment DC.
Answer:
2/3.
Step-by-step explanation:
The 2 triangles are similar so their corresponding sides are in same ratio.
The sides BA and CD are collinear so theire slopes are the same.
Slope of BA = rise/run = 2/3 so slope of DC is also 2/3.
Points D, B, and E are collinear. Find the value of a so that points A, B, and C
are collinear.
Answer: x = 14
Step-by-step explanation:
For points A, B, and C to be collinear, angle ABD and EBC must be vertical angles. Vertical angles are congruent so we will set them equal to each other and solve for x.
Given:
126 = 9x
Divide both sides of the equation by 9:
14 = x
Reflexive property:
x = 14
Please help me find the circumference of the circle!
Answer:
[tex]C=59.6902604182[/tex]
Step-by-step explanation:
The formula to calculate the circumference of a circle given the diameter is:
[tex]C=\pi d[/tex]
Substitute and solve:
[tex]C=\pi \times19=59.6902604182[/tex]
[tex]C=59.6902604182[/tex]
Since the question doesn't say to round your answer is "59.6902604182."
Hope this helps.
Sara had 222 dollars to spend on 9 books after buying then she had 15 dollars how much did each book cost
Answer:
each book cost=222-15=207/9=22.88 dollar
The wind force f on a sail varies jointly as the area a of the sail and the square of the wind speed w. The force on a sail with an area of 500 ft^2 is 64. 8 pounds when the wind speed is 18 mph. What would be the force for a sail with an area of 250 ft^2 with a wind speed of 35 mph
Answer:
122.5 pounds.
Step-by-step explanation:
f = kaw^2
So, k = f/aw^2
From the given data:
k = 64.8/(500*18)
= 0.0004
When a = 250 and w = 35:
f = 0.0004*250*35^2
= 122.5
Is the triangle formed by points A, B, and C a right triangle?
Answer:Yes
Step-by-step explanation: It is a right triangle as if you imagine it, you can see that is half of a square, holding a right angle within it.
Of the teacups in Isabella's Tea Shop, 1/3 are indigo and another 1/4 are orange. What fraction of the teacups are either indigo or orange?
The fraction of the teacups that are either indigo or orange is 7/12.
What is a fraction?A fraction refers to a part of a whole number. It is a proportional value.
A fraction is a quotient that results from a division operation when the numerator is divided by the denominator.
In a proper fraction, the numerator is smaller than the denominator. This is not the case with improper fractions where the numerator is larger than the denominator.
There are complex, proper, and improper fractions.
The fraction of teacups that are indigo = 1/3
The fraction of teacups that are orange = 1/4
The fraction that are either indigo or orange = 7/12 (1/3 + 1/4)
Thus, the fraction or proportion of the Tea Shop's teacups that are either indigo or orange is 7/12.
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The points (p, -2) and (6, 8) fall on a line with a slope of -10. What is the value of p?
Thank you!
Step-by-step explanation:
(8 + 2)/(6 - p)= -10
10/6 - p = -10
-60 + 10p = 10
10p= 70
p= 7
How do you solve 7x 5y?
We can solve the given linear equation 7x = 5y by plotting the graph of x and y on the coordinate plane.
An equation is known to be a linear equation in two variables if it is written in the form of ax + by + c = 0, where a, b and c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.
First, solve for x
7x = 5y
Divide both sides by 7
7/7 x = 5/7 y
Dividing by 7 undergoes the multiplication by 7
x = 5/7 y
Similarly, solve for y
7x = 5y
Divide both sides by 5
7/5 x = 5/5 y
Dividing by 5 undergoes the multiplication by 5
y = 7/5 x
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L)
express the given in terms os sin x or cos x
sin ( 4pi - x )
how
The value of sin(4π-x) is -sinx
What are trigonometric functions?The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
Given that, express the given in terms of sinx or cosx sin (4π-x)
sin(4π-x) = sin(2π+2π-x)
We know, that, sin(a+b) = sina·cosb+sinb·cosa
Here, a = 2π and b = 2π-x
Therefore,
sin(2π+2π-x) = sin2πcos(2π-x)+sin(2π-x)cos2π
Now, sin2π = 0 and cos(2π) = 1
Therefore,
sin2πcos(2π-x)+sin(2π-x)cos2π
= sin(2π-x)
As we know that, sin(2π-x) = -sinx
Hence, sin(4π-x) = -sinx
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During a sale, a store offered a 20% discount on a tablet computer that originally sold for $490. After the sale, the discounted price of the tablet computer was marked up by 20%. What was the price of the tablet computer after the markup? Round to the nearest cent.
Step-by-step explanation:
I think you have to change 20% to a fraction
Think back to the pyramids in Egypt. For a Social Studies project, you created a scale figure of one pyramid. The dimensions are shown. How much paint will you need to paint the entire pyramid for your project?
The surface area of the pyramid is 568 square inches.
What is the surface area of a square pyramid?The surface area of the square pyramid is defined as the total area covered by the surfaces required to make the square pyramid. The area is the space occupied by the square pyramid in two-dimensional planes.
The formula to calculate surface area will be calculated by the formula below,
SA=B+12(P × l)
Here, B is the area of the base, P is the perimeter of the base, and l is the slant height.
SA = ( 8 x 8 ) + 12 ( 8 x 4 + 10 )
SA = 64 + 12 ( 32 + 10 )
SA = 64 + 12 x 42
SA = 568 square inches
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Solve the following problems, please
1) G+7 = 4
2) -5a = 10
3) S-9=10
4) F+15=3
5) -8d = -64
6) A/7 = -4 (divided = /)
7)W-5 =7
Answer:
1. g=-3
2. a=-2
3. s=19
4. f=-12
5.d=8
6.a=-28
7.w=12
Step-by-step explanation:
1) take 4-7 to get -3
2) take 10 divided by -5 to get -2
3) take 10+9 to get 19
4) take 3-15 to get -12
5) take -64 divided by -8 to get 8
6) take -4 times 7 to get -28
7)take 7 plus 5 to get 12
Use logarithmic table to evaluate 40.79÷0.003949
Answer:
1.033×10⁴
Step-by-step explanation:
You want the quotient 40.79÷0.003949 using log tables.
Log of quotientThe log of a quotient is the difference of logs:
log(a/b) = log(a) -log(b)
Log valuesIt can work well to start by writing the numbers in scientific notation:
log(40.79) = log(4.079×10¹) = 1 +log(4.079) = 1.6106
log(0.003949) = log(3.949×10⁻³) = -3 +log(3.949) = -3 +0.5965
Log of quotientThen the log of the quotient is ...
log(40.79/0.003949) = 1.6106 -(-3 +0.5965) = 4.0141
AntilogThe antilog of this number will be ...
antilog(4.0141) = 10⁴ × antilog(0.0141) ≈ 1.033×10⁴
With our 4-digit log tables, 4 significant figures is the best we can expect.
The quotient is about 1.033×10⁴.
__
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