You deposit $2000 each year into an account earning 7% interest compounded annually. How much will you have in the account in 30 years?
The amount that will be in the account after 30 years is $188,921.57.
How much would be in the account after 30 years?When an amount is compounded annually, it means that once a year, the amount invested and the interest already accrued increases in value. Compound interest leads to a higher value of deposit when compared with simple interest, where only the amount deposited increases in value once a year.
The formula that can be used to determine the future value of the deposit in 30 years is : annuity factor x yearly deposit
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r = interest rate n = number of years$2000 x [{(1.07^30) - 1} / 0.07] = $188,921.57
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does this represent two quantities that are proportional
Answer:
from looking at this we can see
1*4=4
2*4=8
3*4=12
6*4=24
a
Hope This Helps!!!
Josue has a coin collection. He keeps 11 of the coins in his box, which is 5% of the collection. How many total coins are in his collection?
Answer:
220
Step-by-step explanation :
11 = 5%
100 ÷ 5 = 20
11 × 20 = 220
0.05 × 220 = 11 ✓
0.05 = decimal multiplier of 5%
Solve the following equation. Write your answer in reduced fraction form, if necessary. (7x−2)(x+6)=0
Answer:
x = 2/7
x = -6
Step-by-step explanation:
You can solve the equation by setting each set of parentheses equal to 0 and simplifying.
7x - 2 = 0 <----- First set of parentheses
7x = 2 <----- Add 2 to both sides
x = 2/7 <----- Divide both sides by 7
x + 6 = 0 <----- Second set of parentheses
x = -6 <----- Subtract 6 from both sides
choose the correct option that explains what steps were followed to obtain the system of equations below x+6y = 5
To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by -3. The solution of system B will be the same as the solution of system A.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
System A:
x + 6y = 5 and; 3x - 7y = -35
To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by -3.
System B:
x + 6y = 5 and; - 25y = -50
The solution of system B will be the same as the solution of system A.
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What will it cost to carpet a rectangular floor measuring 21 feet by 18 feet if the carpet costs $25.68 per square yard?
$1078.56
What is the formula of the area of the rectangle?The formula of the area of the rectangle = Length * Breadth
= 18*21 feet
= 378 feet^2
As cost of carpet is given in square yard. so convert area of rectangle in square yard.
1 square feet = 9 square yard
so, 378/9 = 42 square yard
Cost of carpet = $ 25.68 per square yard (given)
Total cost of rectangular floor = 25.68 * 42
= $1078.56 square yard
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$1078.56 is the cost to carpet a rectangular floor measuring 21 feet by 18 feet if the carpet costs $25.68 per square yard.
What will it cost to carpet a rectangular floor?Given:
A rectangular floor measuring 21 feet by 18 feet.The carpets cost $25.68 per square yard.Find:
Cost to carpet a rectangular floor.Solution:
The formula of the area of the rectangle = Length * Breadth
= 18*21 feet
= 378 feet^2
As the cost of the carpet is given in square yard. so convert an area of the rectangle into a square yard.
1 square foot = 9 square yards
so, 378/9 = 42 square yard
Cost of carpet = $ 25.68 per square yard (given)
Total cost of rectangular floor = 25.68 * 42
= $1078.56 square yard
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please help with this question
The value of angle TUS based on the information given about the circle will be 49°.
What is a circle?It should be noted that a circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
Equivalently, a circle is the curve traced out by a point that moves in a plane so that its distance from a given point is constant.
The radius is the line segment extending from the center of a circle or sphere to the circumference or bounding surface.
Here, the value of TUS will be:
= 1/2 × TRS
= 1/2 × 98°
= 49°
In conclusion, the correct option is 49°.
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Complete question:
Circle R has a radius of 6 inches. Points S, T, and U lie on circle R, clockwise in alphabetical order. If m∠TRS = 98°, what is m∠TUS?
An insurance company study shows that 9% of U. S. adults have diabetes. Suppose 8 US adults are selected at random. LetX be the number of US adults among the 8 selected that have diabetes. Find the mean and standard deviation of X.
Using the binomial distribution, it is found that:
The mean of X is of 0.72.The standard deviation of X is of 0.81.What is the binomial probability distribution?It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The expected value of the binomial distribution is:
E(X) = np
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
For this problem, the parameters are given as follows:
n = 8, p = 0.09.
Hence the mean and the standard deviation are, respectively:
E(X) = np = 8 x 0.09 = 0.72.[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{8 \times 0.09 \times 0.91} = 0.81[/tex]More can be learned about the binomial distribution at https://brainly.com/question/24863377
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What fraction with a denominator of 32 is equal to 1/2?
Answer:
[tex]\frac{16}{32}[/tex]
Step-by-step explanation:
given
[tex]\frac{1}{2}[/tex] ← multiply numerator and denominator by 16 (2 × 16 = 32 )
= [tex]\frac{16}{32}[/tex]
Find an angle between 0 and 360 that is coterminal with -60.
The angle which is coterminal with -60 between 0 and 360 is; 300°.
Which angle is coterminal with -60?Since, it follows that the representation of the angle -60 corresponds to 60° span in the clockwise direction.
Therefore, by going the conventional anticlockwise direction, the angle which is coterminal with -60 is; 300°.
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HELLO! I need aid with my assignment please, all the equations and to be solved. Please!
By using excel sheet we can get the answers for the difference t test.
The two kinds of formula are used in the excel . One from the data analysis the t test assuming equal variances as nothing was mentioned.
But if the t test for the means is used there might be slight variation in the values.
The other formula was of descriptive statistics.
The data was
No of feedback (sec) Feedback (sec) Difference
45 54 9
33 50 17
59 58 -1
32 38 6
30 42 12
27 35 8
29 38 9
59 66 7
64 65 1
38 55 17
For values between 3.6 and 13.2 we are 95% confident that there is no difference between the means of two given data values.
The null hypothesis is accepted because t stat= -1.322 is less than t critical which is t critical= ±2.119 and lies in the acceptance region.
The p- value is 2.04 which is greater than alpha= 0.05
The t stat for 0.01= 4.561578674 and t Critical two-tail 3.249835541
The t stat is greater than t critical at alpha 0.01 so it is rejected.
The difference t test gives
Count=N 9 9
Mean 41.2 49.67
Mean Difference 8.4
Standard Deviation 14.967 11.97
Variance 223.944 143.25
Standard Error 2.0824
t = -1.322
df = 16
t Critical two-tail 2.119905285
Confidence Level(95.0%) 4.802039614
Lower CI (95.0%) = 3.6
Upper CI(95.0%)= 13.2
t stat for 0.01= 4.561578674
t Critical two-tail 3.249835541
Confidence Level(99.0%) 6.055710988
Lower CI (99.0%) = 2.345
Upper CI(99.0%)= 14.457
For values between 3.6 and 13.2 we are 95% confident that there is no difference between the means of two given data values.
The null hypothesis is accepted because t stat= -1.322 is less than t critical which is t critical= ±2.119 and lies in the acceptance region.
The p- value is 2.04 which is greater than alpha= 0.05
The t stat for 0.01= 4.561578674 and t Critical two-tail 3.249835541
The t stat is greater than t critical at alpha 0.01 so it is rejected.
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FRAME AN EQUATION AND SOLVE IT. NEED HELP ASAP I only have 5 minutes!
Answer:
The answer to your question is 125
Step-by-step explanation:
x = 25 X 5= 125.
The required number is 125.
I hope this helps and have a good day!
What does the acronym EDI stand for ? a ) Electronic data interchange b ) Electronic duty interruption c ) Estimated duration indication Extreme data interchange d )
electronic data interchange
Which logarithmic equation is equivalent to 82 = 64?
2 = log Subscript 6 Baseline 64
2 = log Subscript 64 Baseline 8
8 = log Subscript 2 Baseline 64
64 = log Subscript 2 Baseline 8
Answer: Choice B
[tex]2 = \log_{8}(64)[/tex]
======================================================
Explanation:
The original equation is [tex]8^2 = 64[/tex] with 8 as the base. That is also the base of the log when we get the final answer shown above. Logs are useful to isolate the exponent.
The general rule is that [tex]\text{y} = b^{\text{x}}[/tex] is equivalent to the log form of [tex]\text{x} = \log_{b}(\text{y})[/tex] where b is the base of each.
2 = log Subscript 64 Baseline 8 is the logarithmic equation which is equivalent to 82 = 64.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
A logarithmic equation is an equation that involves the logarithm of an expression containing a variable.
The logarithmic equation equivalent to 82 = 64 is:
2 = log Subscript 64 Baseline 8
This is because the logarithmic equation relates the base (64) to the result of the exponentiation (8), which in this case is 2.
Hence, 2 = log Subscript 64 Baseline 8 is the logarithmic equation which is equivalent to 82 = 64.
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carl is 7 years older than angela. the sum of five times carl's age and four times angela's age is 197. how old is each now
The ages of Carl and Angela given from the expression is 25 years and 18 years respectively
EquationAngela's age = xCarl's age = x + 7sum of five times carl's age and four times angela's age is 1975(x + 7) + 4x = 197
5x + 35 + 4x = 197
9x = 197 - 35
9x = 162
x = 162/9
x = 18
So,
Angela's age = x
= 18 years
Carl's age = x + 7
= 18 + 7
= 25 years
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101 101 Suppose that Σ ai = -12 and Σ bi = -19. i=1 i=1 Compute the sum. 101 Σ( – 5ai – 12bi) i=1
Distribute the summation over the sum.
[tex]\displaystyle \sum_{i=1}^{101} (-5a_i - 12b_i) = -5 \sum_{i=1}^{101} a_i - 12 \sum_{i=1}^{101} b_i[/tex]
Now plug in the known sums and simplify.
[tex]\displaystyle \sum_{i=1}^{101} (-5a_i - 12b_i) = -5(-12) - 12(-19) = \boxed{288}[/tex]
point(s) possible
Set up a ratio for the following information and reduce to lowest terms: $3 per day for 12 employees for 39 days.
Answer:
3:12:39
Step-by-step explanation:
The ratio of amount for 1 day, number of employee and total number of days is 1 : 4 : 13.
What is ratio?Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.
If a and b are two values, their ratio will be a:b,
Given information are,
Amount for 1 day = $3,
Number of employee = 12,
Total number of days = 39.
The ratio of amount for 1 day, number of employee and total number of days
= 3 : 12 : 39
Simplify the ratio by dividing it to 3,
= 1 : 4 : 13
The required ratio is 1:4:13.
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pls need help
ersrsreerre
The computation shows that the salesman that has the highest total earnings for the three weeks period will be salesman A.
How to compute the value?It should be noted that from the information given, we are given the information about three salesmen and their sales.
The total earnings for salesman A will be:
= (1300 × 3) + 65 × (11 + 14 + 16)
= 3900 + 2730
= 6630
The total earnings for salesman B will be:
= 300 × 3 + 40 × (14 + 15 + 13)
= 900 + 1680
= 2580
The total earnings for salesman C will be:
= 900 × 3
= 2700
Therefore, the computation shows that the salesman that has the highest total earnings for the three weeks period will be salesman A.
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A recent survey points to the transformation underway in the automotive retail landscape. A study found that automobile executives believe the number of physical automotive retail outlets, as we know them today, will be reduced by 30% to 50%. Eighty-two percent of automobile executives strongly agree that the only viable option for physical retail outlets will be the transformation into service factories, used car hubs, or focusing on an ID-management approach, where the customer is recognized at every single touchpoint. What additional information would you want to know about the survey before you accepted the results of the study?
The additional information would you want to know about the survey before you accepted the results of the study will be:
What sampling design was used?What was the population from which the design was selected?What was the response rate?How to illustrate the information?In research of human subjects, a survey is a list of questions aimed for extracting specific data from a particular group of people.
Surveys may be conducted by phone, mail, through the internet or in malls. From the information, a recent survey points to the transformation underway in the automotive retail landscape.
It is important to know the sampling design that was used, the population from which the design was selected and the response rate.
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PLS I NEED HELP
2. Write the rule for the linear function. Remember a function rule is written using f(x).
Answer:
[tex]f(x) = \frac{1}{2}x + 5[/tex]
Step-by-step explanation:
So you can generally express a linear function use the slope-intercept form as such: [tex]y=mx+b[/tex] where m=slope, and b=y-intercept.
The y-intercept is defined as the value of f(0), since when the line crosses the y-axis, the x-value is 0, and as provided in the table that value is 5, so we have the function rule: [tex]f(x) = mx+5[/tex]
The slope is defined as how much y-changes, as x increases by 1. We can generally use the formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] and this can be found using any two points, since the slope is constant.
We can use the two points (0, 5) and (2, 6) and plug it into the equation, to find the rise/run
[tex]\frac{6-5}{2-0} = \frac{1}{2}[/tex]
So plugging this into the slope-intercept form you get the function
[tex]f(x) = \frac{1}{2}x + 5[/tex]
Adam eats 20 % of a pizza, Bethany eats another 1/3 of the pizza, and Charlie eats the remaining 14 slices. How many slices total did the pizza originally have?
The pizza originally have 30 slices.
What is linear equation?
An equation in which the highest power of the variable is one is known as linear equation.
We will find number of pizza slices as shown below:
Let pizza originally have x slices.
Adam eats 20% of a pizza
= 0.2x
Bethany eats 1/3 of pizza
=1/3(x)
Charlie eats the remaining 14 slices
0.2x+1/3(x)+14=x
14 = x - 0.2x - 1/3(x)
14 = x - x/5 - x/3
14 = (15x - 3x - 5x)/15
14*15 = 7x
By dividing both sides by 7, we get
30 = x
x = 30
Hence, the pizza originally have 30 slices.
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Which term has a degree of 8?
A.8xy
OB. -22³5
OC. 9ry
OD. 3x²y4
The term that has a degree of 8 is -2x³y⁵
How to find the degree of a polynomial?The polynomial above is a monomial. A monomial is a polynomial with a single term.
Therefore, the degree of a monomial is the sum of the exponents of all its variables.
In other words, a monomial is a number, a variable or a product of a number and a variable where all exponents are whole numbers.
Hence, the term with degree of 8 is -2x³y⁵
Degree = 0 + 3 + 5 = 8
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Refer to the figure below.
BED and CEA are
angles.
A
C
E
D
B
Answer:
both two
Step-by-step explanation:
because it is in alphabetical order
Translate to a proportion and solve.
148.5 is 59 1/5% of what?
The actual value is 250.
Applying simple percentage formula here,
let x be the whole value
x=148.5/ 59 2/5%
x= 148.5/0.594
x=250.
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The actual value is 250.
Applying percentage formula here,
let x be the value:
x=148.5/ 59 2/5%
x= 148.5/0.594
x=250
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Geometry question please help!
Answer:
4
Step-by-step explanation:
Since,
The width of the Longer gear is 7, and the smaller gear has a width of 3..
7-3 = 4
Hope it helps...
Marking me as Brainliest would help me... :(
Could you help me solve?
Answer:
1.14200738982×10^26
Step-by-step explanation:
Substitution can make this integral much easier to evaluate.
SubstitutionLet u = 7x² -x. Then du = (14x -1)dx. The limits on x become different limits for u:
for x = 1: u = 7(1²) -1 = 6
for x = 3: u = 7(3²) -3 = 60
Integral[tex]\displaystyle\int_1^3{(14x-1)e^{(7x^2-x)}}\,dx=\int_6^{60}{e^u}\,du=\left.e^u\right|^{60}_6\\\\=e^{60}-e^6\approx e^{60}\approx\boxed{1.14200738982\times10^{26}}[/tex]
use technology to determine an approximate solution to each of the following systems of linear equations
a y=22x-9.5 and y=2.5x+4.1
b 8x+y-18=0 and 5x+9y+4=0
c 6x + y= 12 and 5x +8y =-100
From the given system of linear equations, we have;
a. x ≈ 0.697, y ≈ 5.84b. x ≈ 2.48, y ≈ -1.82c. x ≈ 4.56, y ≈ -15.35How can technology be used to solve the given equations?a. The system of linear equations can be expressed as follows;
y = 22•x - 9.5
y = 2.5•x + 4.1
Rewriting the equations to have the constants on the right, we have;
y - 22•x = - 9.5
y - 2.5•x = 4.1
Solving the above equations using matrices method on a calculator gives;
y = 5.84x = 0.697By direct solving, we have;
22•x - 9.5 = 2.5•x + 4.1
22•x - 2.5•x = 4.1 + 9.5
19.5•x = 13.6
x = 13.6 ÷ 19.5 ≈ 0.697
x ≈ 0.697y = 22•x - 9.5
y = 22×(13.6/19.5) - 9.5 ≈ 5.84
y ≈ 5.84b. 8•x + y - 18 = 0
5•x + 9•y + 4 = 0
Rewriting gives;
8•x + y = 18
5•x + 9•y = -4
Solving with technology gives,;
x ≈ 2.48y ≈ -1.82Solving directly gives;
y = 18 - 8•xy = -(5•x + 4)/9Which gives;
18 - 8•x = -(5•x + 4)/9
9×(18 - 8•x) = -(5•x + 4)
162 - 72•x = -(5•x + 4)
5•x - 72•x = -162 - 4 = -166
67•x = 166
x = 166 ÷ 67 ≈ 2.478
x ≈ 2.478y = 18 - 8•x
Therefore;
y = 18 - 8 × (166 ÷ 67) ≈ -1.82
y ≈ -1.82c. 6•x + y = 12
5•x + 8•y = -100
Solving the above linear system using technology, we have;
x ≈ 4.56y ≈ -15.35Solving directly, we have;
y = 12 - 6•x
5•x + 8•y = -100
y = (-100 - 5•x)/8
12 - 6•x = (-100 - 5•x)/8
8 × (12 - 6•x) = (-100 - 5•x)
96 - 48•x = (-100 - 5•x)
48•x - 5•x = 96 + 100
43•x = 196
x = 196/43 ≈ 4.56
x ≈ 4.56y = 12 - 6•x
Therefore;
y = 12 - 6×(196/43) ≈ -15.35
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Simplify the problem
Answer:
B. 2√3+4
Step-by-step explanation:
3√3+4−√3
=2√3+4 (Decimal: 7.464102)
here is a polygon. draw a scaled copy of the polycon with scale factor 3
The scaled copy of the polygon is added as an attachment
How to draw the scaled copy?The complete question is added as an attachment
The coordinates of the polygon are
A = (-7, 6)
B = (-10, 8)
C = (-10, 10)
D = (-6, 10)
The scale factor is 3.
So, the rule of dilation is
(x, y) = (3x, 3y)
Using the above rule, we have:
A' = (-21, 18)
B' = (-30, 24)
C' = (-30, 30)
D' = (-18, 30)
See attachment for the scaled copy of the polygon
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In the figure below, the radius of the larger circle is 6,8 and the radius of the smaller circle is 4.5. Which of the following best approximates the area of the shaded region? Note: The figure is not drawn to scale. O 14.45 O 16.62 O 25.99 O 81.65 O 145.27
A circle is a figure bounded by a curved side which is referred to as circumference. Thus the area of the shaded region is option D. 81.65.
A circle is a figure bounded by a curved side which is referred to as circumference. Some of its parts are radius, diameter, sector, arc, etc.
The area of a circle can be determined by the given expression:
Area = π[tex]r^{2}[/tex]
where r is the radius of the circle and π = [tex]\frac{22}{7}[/tex]
So, the area of the shaded region can be determined as:
Area of the shaded region = area of the larger circle - area of the smaller circle
Area of the shaded region = π[tex](6.8)^{2}[/tex] - π[tex](4.5)^{2}[/tex]
= π (46.24 - 20.25)
= [tex]\frac{22}{7}[/tex] x 25.99
= [tex]\frac{571.78}{7}[/tex]
Area of the shaded region = 81.683
Thus the appropriate answer to the question is option D. 81.65.
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