The simple interest earned on a 2,000 principal at 8% interest for 5 years is I = $1,937.50.
What is meant by simple interest formula?Simple interest is calculated by multiplying the daily interest rate by the principal and the number of days between payments. Customers who pay their loans on time or early each month save money on interest.Interest-only loans are prevalent for short-term personal loans and car loans. Simply multiply the principal amount by the interest rate and the time to determine simple interest.The written formula is "Simple Interest = Principal x Interest Rate x Time." Simple interest is calculated on the loan principal or the first deposit into a savings account.Due to the fact that simple interest does not compound, a creditor will only pay interest on the principal amount, and a borrower will never be required to pay interest on previously accumulated interest.Therefore,
I = Prt
First, converting R percent to r a decimal
r = R/100 = 3.875%/100 = 0.03875 per year,
then, solving our equation
I = 10000 × 0.03875 × 5 = 1937.5
I = $ 1,937.50
The simple interest accumulated
on a principal of $ 10,000.00
at a rate of 3.875% per year
for 5 years is $ 1,937.50.
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What is the y-intercept of the function y = log4 (2x+64) +3?
Answer:
(0, 6)
Step-by-step explanation:
Given function:
[tex]y=\log_4(2x+64)+3[/tex]
The y-intercept of a function is the point at which the curve crosses the y-axis, so when x = 0.
Therefore, to find the y-intercept, substitute x = 0 into the function:
[tex]\implies y=\log_4(2(0)+64)+3[/tex]
[tex]\implies y=\log_4(64)+3[/tex]
Rewrite 64 as 4³:
[tex]\implies y=\log_4(4)^3+3[/tex]
[tex]\textsf{Apply the log power law}: \quad \log_ax^n=n\log_ax[/tex]
[tex]\implies y=3\log_4(4)+3[/tex]
[tex]\textsf{Apply log law}: \quad \log_aa=1[/tex]
[tex]\implies y=3(1)+3[/tex]
[tex]\implies y=3+3[/tex]
[tex]\implies y=6[/tex]
Therefore, the y-intercept of the given function is (0, 6).
a lottery consists of selecting 5 numbers out of 45 numbers. you win $10 if exactly three of your 5 numbers are matched to the winning numbers chosen. what is the probability of winning the $10? round your answer to six decimal places.
With the help of probability we can conclude our answer.
What is probability?The area of mathematics known as probability deals with numerical representations 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, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.acc to our question-,
first number: 1/25 chance because we only want 1 out of the 25 possibilities.Second number: 1/24 because 1 number was already taken out.Third: 1/23Fourth: 1/22Fifth: 1/21Sixth: 1/20The chance of all of these events happening right after another is 1/25 x 1/24 x 1/23 x 1/22 x 1/21 x 1/20 = 1/127512000, or about 1 in a hundred million.learn more about probability click here:
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a sleep time of 15.9 hours per day for a newborn baby is at the 10th percentile of the distribution of sleep times for all newborn babies. assuming the distribution is normal with standard deviation 0.5 hour, approximately what is the mean sleep time, in hours per day, for newborn babies? responses 15.1 15.1 15.3 15.3 16.3 16.3
The mean sleep time is 16.54 hours per day for newborn babies
What is mean?In mathematics and statistics, the concept of mean is crucial. The most typical or average value among a group of numbers is called the mean.It is a statistical measure of a probability distribution's central tendency along the median and mode. It also goes by the name "anticipated value."It is a statistical idea with significant financial implications. The idea is applied in a number of financial areas, such as business appraisal and portfolio management, although not exclusively.acc to our question-
z-score = (x - μ)/σ, where x is the score , μ is the mean and σ is thestandard deviationA sleep time of 15.9 hours per day for a newborn babyx = 15.9 hoursAt the 10th percentile of the distribution of sleep times for all newborn babiesThat means we want to find z-score corresponding to 0.1 (10/100 = 0.1)By using the normal distribution tablez = -1.28The standard deviation is 0.5 hourσ = 0.5Substitute these values in the rule above-1.28 = (15.9 - μ)/0.5Multiply both sides by 0.5-0.64 = 15.9 - μAdd μ to both sides-0.64 + μ = 15.9add -0.64 to both sidesμ = 15.9 + 0.64 = 16.54The mean sleep time is 16.54 hours per day for newborn babies.
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What is a,b,c and day
[tex]a=-5(-3)-2=13\\\\b=-5(-1)-2=3\\\\c=-5(1)-2=-7\\\\d=-5(2)-2=-12[/tex]
Answer:
A = 13 B = 3 C = -7 D = -12
Step-by-step explanation:
Just insert the x values for a, b, c, and d. for example if we were to find a.
The x value for a is -3 so we would put -3 in place of x in the equation.
-5(-3) - 2
Remember: Two negative numbers multiplied with each other equal a positive.
15 - 2 = 13
I'm not sure I need help.
Answer:
A
Step-by-step explanation:
It is perpendicular because it forms a right angle with the second line
White shapes and black shapes are used in a game.
Some of the shapes are circles.
All the other shapes are squares.
The ratio of the number of white shapes to the number of black shapes is 7:3
The ratio of the number of white circles to the number of white squares is 2:7
The ratio of the number of black circles to the number of black squares is 1:2
Work out what fraction of all the shapes are circles.
Give your answer as a fraction in its simplest form.
(Hint: Fractions can be written in the form a/b. eg [tex]\frac{5}{28}[/tex] would be written as 5/28)
The fraction of all the circles in the shapes is 23/90
How to calculate the fraction of all the shapes are circles?Given that the:
Ratio of the number of white shapes to the number of black shapes is 7:3
Ratio of the number of white circles to the number of white squares is 2:7
Ratio of the number of black circles to the number of black squares is 1:2
Total share for both white and black shape = 7+3 = 10
share for white shape = 7/10 and share for black shape = 3/10
Total share for white circles and white squares = 2+7 = 9
share for white circles = 2/9 and share for white squares = 7/9
Total share for black circles and black squares = 1+2 =3
share for black circles = 1/3 and share for black squares = 2/3
White circles will take 2/9 of white colors i.e. 2/9 x 7/10 = 14/90 = 7/45
Black circles will take 1/3 of black colors i.e. 1/3 x 3/10 = 3/30 = 1/10
Fraction of circles = 7/45 + 1/10
= 14+9/ 90
= 23/90
Therefore, the fraction of all the shapes that are circles is 23/90
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help me please please please 33333
please helpppp!!!!!!!
Answer:
A
Step-by-step explanation:
function because for every x there is only one y
the domain are the value of x
the range are the value of y
A soft drink manufacturer has a daily production cost of C = 70,000 - 120x + 0.055x ^ 2 , where C is the total cost (in dollars) and x is the number of units produced. How many units should they produce each day to yield a minimum cost?
Show all work please.
They should produce 1091 units each day to yield a minimum cost.
What is the vertex formula?
When the graph crosses its symmetry axes, the vertex formula aids in determining the vertex coordinate of a parabola. The vertex point is often represented by (h, k).
We know that a parabola's conventional equation is y=ax²+bx+c. The vertex in this case should be near the base of the U-shaped curve if the coefficient of x² is positive. The vertex should be at the peak of the U-shaped curve if the coefficient of x² is negative.
We have,
C = 70,000 - 120x + 0.055x²
C = 0.055x² - 120x + 70,000
Hence, for this equation, the graph will be parabola opening upward.
For that, the vertex will be the minimum cost
x = (-b) / 2a
Here, a = 0.055 , b = -120
Now, find and put the values of x.
minimum cost (x) = ( -(-120) ) ÷ ( 2 × 0.055 )
= 120 ÷ 0.11
= 120 ÷ 0.11
= 1090.90 ≈ 1091 units
The minimum cost will be yield for 1091 units.
Therefore, They should produce 1091 units each day to yield a minimum cost.
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the honda civic hybrid gets 46 miles per gallon in city driving and 51 mpg in highway driving. the car is driven 621 miles in 13 gallons of gasoline. how many miles were driven in the city and how many were driven on the highway?
The distance driven in city is 386.4 miles and same in highway is 213.6 miles.
Let the distance driven in city be x and driven in highway be y.
Now given that the mileage in city is 46 miles per gallon and in highway same is 51 miles per gallon.
The car is driven 621 miles in 13 gallon.
So suitable system of linear equations in two variables to solve this is,
x+y = 621 ……(1)
x/46+y/51 = 13 …….(2)
From (2) we get,
51x+46y = 30498
5x+46(x+y) = 30498
5x+46*621 = 30498
5x = 30498-28566
5x = 1932
x = 386.4
So from (1) we get,
y = 621-x = 621-386.4 = 213.6
Hence the car drove 386.4 miles in city and 213.6 miles in highway.
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What is the surface area of the cuboid below? Remember to give the correct units.
Answer:
surface area=2(lb+lh+bh)
surface area=2(9)(4)+(9)(12)+(4)(12)
surface area=384cm2
You measure containers for international shipments. The height of the standard container is 6 feet and 7 inches. Which of the following is closest to its height in meters?
Josiah read 28 pages in 1 3/5 hours. At what rate, in pages per hour, did he read?
PLEASE HELP!!!!
Josiah read at the rate of 17.5 pages per hour.
What is the speed of reading?Speed of reading is the number of pages read per hour.
Given here, Josiah read 28 pages in 1 ³/₅ hours which is in mixed fraction
now 1 ³/₅ = ⁸/₅ = 1.6 hours
therefore the speed of reading is = 28 / 1.6 = 17.5 pages hour.
Hence, Josiah's the speed of reading is 17.5 pages hour.
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PLEASE HELP I WILL GIVE BRAINLY!!!Question 2(Multiple Choice Worth 2 points)
(Factoring Algebraic Expressions LC)
Rewrite 30 - 6x³ using a common factor.
O2(15-3x³)
O 2x(15-3x²)
O6(5-6x³)
O6x(5-x²)
Answer:
(15-3x³) is the answer.
Step-by-step explanation:
2*15-2*3x³
which is 30-6x³.
Please help! I need help solving this final problem for geometry.
for each of the following determine the n -unit percent change. the 19-unit percent change is 45 %. what is the 17-unit percent change? % the 16-unit percent change is 43 %. what is the 12-unit percent change? % the 20-unit percent change is -25 %. what is the 18-unit percent change? % the 5-unit percent change is -50 %. what is the 8-unit percent change?
Hence, 17-unit percent change is (45/19)×17% = 40.26%
12-unit percent change is (43/16)×12% = 32.25%
18-unit percent change is (-25/20)×18% = -22.5%
8-unit percent change is (-50/5)×8% = -80%
Given, that
The 19-unit percent change is 45 %
Now, 1-unit percent change is 45/19
17-unit percent change is (45/19)×17%
= 40.26%
The 16-unit percent change is 43 %
Now, 1-unit percent change is 43/16
12-unit percent change is (43/16)×12%
= 32.25%
The 20-unit percent change is -25%
Now, 1-unit percent change is -25/20
18-unit percent change is (-25/20)×18%
= -22.5%
The 5-unit percent change is -50 %
Now, 1-unit percent change is -50/5
8-unit percent change is (-50/5)×8%
= -80%
Hence, 17-unit percent change is (45/19)×17% = 40.26%
12-unit percent change is (43/16)×12% = 32.25%
18-unit percent change is (-25/20)×18% = -22.5%
8-unit percent change is (-50/5)×8% = -80%
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If a person spins a six-space spinner and then flips a coin, describe the sample space of possible outcomes using 1, 2, 3, 4, 5, 6 for the spinner outcomes and H, T for the coin outcomes.
The sample space is S={__}
(Use a comma to separate answers as needed.)
Answer:
Step-by-step explanation:
If one spins a six-space spinner and then flips a coin, then the sample space (S) of possible outcomes using (1, 2, 3, 4, 5, 6) for the spinner outcomes and (H, T) for the coin outcomes will be [S = {(1H), (1T), (2H), (2T), (3H), (3T), (4H), (4T), (5H), (5T), (6H), (6T)}]
As per the question statement, a person spins a six-space spinner and then flips a coin,
And we are required to determine the sample space (S) of possible outcomes using (1, 2, 3, 4, 5, 6) for the spinner outcomes and (H, T) for the coin outcomes.
Now, on spinning a six-space spinner, any one of the 6 faces will come as outcomes, and if these outcomes are denoted by (1, 2, 3, 4, 5, 6).
And after spinning the six-space spinner, if one flips a coin, either of "heads" face or "tails" face will come as outcome, which can be denoted by {H, T}.
Therefore, If one spins a six-space spinner and then flips a coin successively as mentioned above, every possible outcome of the spinner will be accompanied by one of two the possible outcomes the coin. Hence, the sample space (S) of possible outcomes will be [S = {(1H), (1T), (2H), (2T), (3H), (3T), (4H), (4T), (5H), (5T), (6H), (6T)}]
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HELP!!
If a₁ = 3 and an
-
= (an-1)2 + 1 then find the value of a4.
The required value of a₄ is 10,202 to the given recursive formula.
What is an arithmetic sequence?An arithmetic sequence is defined as an arrangement of numbers that is in a particular order.
The given recursive formula in the question as:
aₙ = (aₙ ₋₁ )² + 1 ....(i)
And, a₁ = 3
Substitute the value of a₁ = 3 in equation (i), and solve for n = 2
a₂ = (a₁)² + 1
a₂ = (3)² + 1
a₂ = 9 + 1 = 10
Substitute the value of a₂ = 10 in equation (i), and solve for n = 3
a₃ = (10)² + 1
a₃ = 100 + 1 = 101
Substitute the value of a₃ = 101 in equation (i), and solve for n = 4
a₄ = (101)² + 1
a₄ = 10,201 + 1
a₄ = 10,202
Therefore, the required value of a₄ is 10,202.
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6y^2 + 7y - 20= 0
solve this quadratic equation using a multiplication frame.
y= -4/3=-1.333
y= 5/2=2.500
a bank wishes to estimate the mean credit card balance owed by its customers. the population standard deviation is estimated to be $300. if a 98% confidence interval is used and an margin of error of $75 is desired, how many customers should be sampled?
Using a 98% confidence interval, the total number of customers that should be sampled is 87.
What exactly is sample size?The sample size refers to the number of observations in the data set, and as the sample size increases, the calculated value of population parameters becomes more reliable and true. In other words, as sample size increases, the value of the margin of error decreases.
Given,
Standard deviation σ=300
Confidence level: 0.98
Maximum allowable error: ε=75
The critical value is calculated using the standard normal table at the level of significance (0.02)
The critical value in this case is 2.326.
Sample size is calculated by,
n=((Z[tex]z_{\alpha /2}[/tex])²×σ²))/ε²
n=((2.326)²×(300)²)/(75)²
n=86.564≈87
Therefore, the required sample size is 87.
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Please help me I don’t get it
Step-by-step explanation:
3.
we need to find the map size based on actual miles.
so, we find how many map ft are 1 actual mile :
5 ft / 20.5 corresponds to 1 actual mile.
5 / 20.5 = 10/41 ft
now, we have 15.5 actual miles, that is 15.5 times the 1 standard actual mile.
and so, this is
10/41 × 15.5 = 155/41 = 3.7804878048780... map ft
4.
30.5 model cm = 70.6 actual m
1 model cm = 70.6/30.5 = 2.314754098... actual m.
8 model cm = 8×2.314754098... =
= 18.51803279... actual m
5.
7 map m = 14 actual miles
1 map m = 14/7 = 2 actual miles.
14 map m = 14×2 = 28 actual miles.
6.
8 map km = 6 actual miles
we need to calculate the map km, so we need the standard actual mile
1 actual mile = 8/6 = 4/3 = 1.3333333... map km.
50.2 actual miles = 50.2×1.333333... =
= 66.93333333... map km.
7.
80.2 model cm = 40.2 actual m
1 model cm = 40.2/80.2 = 0.501246883... actual m
10 model cm = 10×0.501246883... =
= 5.01246883... actual m
8.
6 map m = 15 actual miles
1 map m = 15/6 = 5/2 = 2.5 actual miles
8.8 map m = 8.8×2.5 = 22 actual miles
9.
5 map ft = 16.5 actual miles
1 actual mile = 5/16.5 = 0.303030303... map ft
45.6 actual miles = 45.6×0.303030303... =
= 13.81818181... map ft
10.
65.8 model cm = 95.6 actual m
1 model cm = 95.6/65.8 = 1.452887538... actual m
12 model cm = 12×1.452887538... =
= 17.43465046... actual m
A theatre contains 439 seats and the ticket prices for a recent play were $48 for adults and $28 for children. if the total proceeds we $15,852 for a sold-out matinee, how many of each type of ticket were sold?
The theatre sold 178 adult tickets and 261 children tickets for the play.
It is given that the total number of seats is 439 seats.
There are two types of tickets available- children and adults.
The price for adult tickets is $48 and that for children is $28.
Let the number of adult tickets sold be x
Let the number of children's tickets sold be y.
The show was a sold-out
Hence,
x + y = 439 [1]
48x + 28y = 15852 [2]
From equation [1] we get
x = 439 - y
putting this result in equation [2] gives us
48(439 - y) + 28y = 15852
or, 21072 - 48y + 28y = 15852
or, -20y = - 5220
or, y = -5220/ -20
or, y = 261
Therefore,
x + 261 = 439
or, x = 439 - 261
or, x = 178
Hence, 178 adult tickets were sold and 261 children's tickets were sold.
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state how the 2 triangles are congruent?? SSS and SAS HELP ASAPPP??
The two triangles are congruent by SAS criterion.
What is SAS criterion?According to this standard, two triangles are said to be congruent if their two sides are equal to the sides of another triangle and their respective angles are also equal. The "Side-Angle-Side" triangle congruence theorem is referred to as the SAS Criterion.According to the Side-Angle-Side theorem of congruency, two sides and the angle they produce are congruent if they are equivalent to two sides and the included angle of another triangle.Verification:
Let's carry out an exercise to demonstrate SAS's validity. AB=PQ, BC=QR, and ∠B=∠Q are given. To demonstrate: ΔABC≅ΔPQRPlacing the triangle ABC over the triangle PQR will cause B to fall on Q and the AB side to coincide with the PQ side.Point A falls on point P because AB=PQ.The side BC will fall along the side QR since ∠B=∠Q.Point C is in line with point R since BC=QR. As a result, BC and QR coincide, while AC and PR coincide.ΔABC will therefore match ΔPQR. Consequently, ΔABC ≅ ΔPQR. This exemplifies the SAS congruence criterion.To learn more about SAS criterion, refer to https://brainly.com/question/22472034
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Identify the correct command to find the derivative ofywith respect toxof the following equation:y=4x∧4−3x∧2+6x+14dydx=polyder([4,0,−3,6],14)dydx=polyder([4,0,−3,6,14])dydx=polyder(4,0,−3,6,14)dydx=polyder([4,−3,6],14) Explanation: When taking the derivative of a polynomial, the coefficients of the polynomial must be arranged in decending powers, being careful to specify zero for missing terms. The constant (i.e.,xto the zero power) is included in the array of coefficients.
The derivative of the given polynomial equation is 16x³ - 6x + 6.
We are given an equation. The equation represents a polynomial in one variable. The degree of the polynomial is four; hence, it is called biquadratic. We need to find the derivative of the given polynomial. The derivative of a function of a real variable in mathematics describes the sensitivity of the function value to a change in its argument. Calculus relies heavily on derivatives.
The equation is given below.
y = 4x^4 - 3x² + 6x + 14
dy/dx = (d/dx)(4x^4 - 3x² + 6x + 14)
dy/dx = (d/dx)(4x^4) - (d/dx)(3x²) + (d/dx)(6x) + (d/dx)(14)
dy/dx = [4*4x^(4 - 1)] - [3*2x^(2 - 1)] + [6*1x^(1 - 0)] + [14*0x^(0 - 1)]
dy/dx = 16x³ - 6x + 6
Hence, the derivative of the given polynomial equation is 16x³ - 6x + 6.
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What is the value of x in the system of equations shown below?
5x+4y=1
y=1-x
Answer:
x=-3
Step-by-step explanation:
we can fill the y into the first equation since we already know what it is equal to
5x+4(1-x)=1
5x+4-4x=1
x+4=1
-4. -4
x=-3
Hopes this helps please mark brainliest
Answer:
5x + 4y = 1
Answer: x = 1/5 - 4y/5
y = 1 - x
Answer: x = −y + 1
Step-by-step explanation:
Please give the brainliest, really appreciated.
n?
8) 2y = 6x²-x+3
2y=6x
8
sy=-15
linear or nonlinear
Answer: I would say non linear. I have done problems like these before and anytime there is an exponent in the equation it always ends up being non linear. Also remember for it to be linear it most form a straight line that passes through the origin.
Step-by-step explanation:
Given a point (5,-6) and slope m = -2
Write the Point-Slope Equation of the line.
Please give me a great explanation and explain like your talking to a baby please. Thanks :)
Answer:
y+6 =-2(x-5)
Step-by-step explanation:
The question is asking for the equation of the line
The equation for point-slope form is always written as y-y₁=m(x-x₁)
y₁ and x₁ are the points given to you in this order (x₁, y₁)
so x₁=5 and y₁=-6
Now you plug in all the numbers you have into the point slope form
y- (-6)= -2(x-5)
When you subtract a negative (a double negative you get a positive)
y+6=-2(x-5)
Point-Slope form is usually the easiest form of a line to write since you do not need to solve for any intercepts or other points. You have y on one side of the equation, usually the left to make it easier to read, and x on the other, usually the right.You subtract the point that you are given from the y and the x. Multiply everything that is on the same side of the equation of the x by the slope (m).
Notes:
For y₁ and x₁, they could be any point on the line. For example, (1,2) is also on this line. So the equation would be
y-2=-2(x-1)
1. Which can be used to prove dit? (1 point)
d
O Transitive Property of Parallel Lines
O Transitive Property of Congruence
O Perpendicular Transversal Theorem
O converse of the Corresponding Angles Postulate
Factorise the following
4x²-25y²
Answer:
= (2x + 5y) * (2x - 5y)
Step-by-step explanation:
4x²-25y²
= (2x)² - (5y)²
= (2x + 5y) * (2x - 5y)
Answer:
[tex]\huge\boxed{\sf (2x + 5y)(2x - 5y)}[/tex]
Step-by-step explanation:
Given expression:[tex]4x^2-25y^2[/tex]
Both of the terms are perfect squares.
[tex](2x)^2-(5y)^2[/tex]
Using formula: a² - b² = (a + b)(a - b)= (2x + 5y)(2x - 5y)
[tex]\rule[225]{225}{2}[/tex]
-7/6 - (-1/9) Evaluate.
- Simplest form.
-1/3 + 5/7 Add.
- Simplest form.
After evaluating those terms,
we get the answer as
1. -7/6 - (-1/9) =[tex]\frac{-19}{18}[/tex]
2. -1/3 + 5/7 = = [tex]\frac{8}{21}[/tex]
What are fractions?A fraction is a number that has a numerator as well as a denominator.
1 / 2 is an example of a fraction. The top part of the fraction is the numerator and the bottom part of the fraction is the denominator.
Fractions represent one value. Dividing the numerator by the denominator shows what decimal value fractions have. For example, 1/2 is equal to 1 ÷ 2 which equals 0.5.
in this we have to evaluate
1. -7/6 - (-1/9)
= [tex]\frac{-7}{6}[/tex] - ([tex]\frac{-1}{9}[/tex])
= [tex]\frac{-21+2}{18}[/tex]
=[tex]\frac{-19}{18}[/tex]
Hence , after solving we get the desired result as -19/18 .
2. -1/3 + 5/7
= [tex]\frac{-1}{3}[/tex] + [tex]\frac{5}{7}[/tex]
= [tex]\frac{-7 + 15}{21}[/tex]
= [tex]\frac{8}{21}[/tex]
Hence, after solving we get the desired result as 8/21 .
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