Answer:
The formula to calculate simple interest is:
I = Prt
Where I is the interest, P is the principal amount borrowed, r is the interest rate per period, and t is the time period.
Using this formula, we can calculate the interest Ms. Lang will pay as follows:
I = Prt
I = 2300 * 0.13 * (30/12)
I = $975
Therefore, Ms. Lang will pay $975 in interest over the 30-month period.
To calculate the total amount she will repay, we need to add the interest to the principal amount borrowed:
Total amount = Principal + Interest
Total amount = $2300 + $975
Total amount = $3275
Therefore, Ms. Lang will repay a total of $3275, which includes the $2300 principal and $975 interest.
now, we're assuming this is on a simple interest rate, so hmm say a year has 12 months, so 30 months will just be 30/12 of a year.
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$2300\\ r=rate\to 13\%\to \frac{13}{100}\dotfill &0.13\\ t=years\to \frac{30}{12}\dotfill &\frac{5}{2} \end{cases} \\\\\\ I = (2300)(0.13)(\frac{5}{2}) \implies I = 747.5~\hfill \underset{ \textit{amount to be repaid} }{\stackrel{ 2300~~ + ~~747.5 }{\text{\LARGE 3047.5}}}[/tex]
The sum of two numbers is 42. The difference of the two numbers is 30. What are the two numbers. Let x be the larger number and y be the smaller number. Write an equation that expresses the information in the sentence 'The sum of two numbers is 42." _____________
Write an equation that expresses the information in the sentence 'The difference of the two numbers is 30." __________
Solve the system you have written above. The larger number, x is ______ The smaller number, y is _____
Answer:
x=36
y=6
system of equations
Note: Picture not drawn to scale.
Given that DE DB and AD CD, which of the following rules could be used to prove ADE CDB?
A.
Side-Side-Side
B.
Side-Angle-Side
C.
Angle-Side-Angle
D.
Angle-Angle-Side
Reset Submit
Triangle Congruence
The rule that could be used to prove that the two triangles are congruent is given as follows:
A. Side - Side - Side.
What is the Side-Side-Side congruence theorem?The Side-Side-Side congruence theorem states that if all three sides of a triangle are congruent (identical) to the corresponding sides of another triangle, then the triangles themselves are also congruent.
For this problem, we have that the two congruent sides are given as follows:
DE and DB.AD and CD.If the third sides are congruent, then the Side-Side-Side congruence theorem can be used.
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What is the area of the shaded part of the following composite figure? Round your answer to the nearest whole.
By adding the rectangle, the shaded area is [tex]53 in^2[/tex], rοunded tο the nearest whole figure.
what is surface area?The entire area οf a three-dimensional οbject's surface is known as surface area. It is a measurement of an οbject's expοsed surface. Indicating an οbject's surface area typically involves using square measurements like square inches οr square meters. The surface area οf a cube, fοr instance, is equal to the tοtal οf the areas οf each οf its six faces. The calculatiοn fοr a cube's surface area is: Surface Area Equals 6*[tex]side^2[/tex] where "side" denοtes the cube's extent οn οne side.
given:
The bigger semicircle has a radius οf 5 inches and a diameter οf 10 inches. Consequently, the bigger semicircle's area is:
(5 in) * (1/2) * π = 39.27 in (rοunded tο twο decimal places)
The smaller semicircle has a radius of οf 2 inches and a width of οf 4 inches. Consequently, the smaller semicircle's size is:
(2 in) * (1/2) * π * 6.28 in (rοunded tο twο decimal places)
The rectangle's area is: because it is 10 inches long and 2 inches wide.
10 in + 2 in equals [tex]20 in ^2.[/tex]
We can add the area οf the rectangle tο the area οf the larger semicircle after subtracting the areas οf the smaller and larger semicircles tο determine the area οf the shaded regiοn:
[tex]39.27 in^2 - 6.28 in^2+ 20 in^2 = 52.99 in^2.[/tex]
By adding the rectangle, the shaded area is 53 in2, rοunded tο the nearest whole figure.
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Teresa runs 6 miles in 44 minutes. At the same rate, how many minutes would she take to run 9 miles?
To find out how many minutes it would take Teresa to run 9 miles at the same rate, we can use a proportion.
We know that Teresa took 44 minutes to run 6 miles. This means she was running at a rate of 6 miles per 44 minutes. To solve for how long it would take to run 9 miles, we can set up a proportion with this information.
Let x = the number of minutes it would take Teresa to run 9 miles.
6/44 = 9/x
Cross-multiply to solve for x: 44x = 54
Divide both sides by 44 to find the solution: x = 54/44 = 1.227 minutes
Therefore, it would take Teresa 1.227 minutes to run 9 miles at the same rate.
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which shows the multiplicative identity property of 1?
A) 4/5 x 1/5 = 1/5 x 4/5
B) 3/8x(1/2x2/3) = (3/8x1/2) x 2/3
C) 1/4x 4= 1
D) 9/10x1=9/10
Option C multiplies one and demonstrates that the result is one, proving that one has the attribute of multiplicative identity.
How is multiplicative identity property of 1 determined?Any number multiplied by one is equal to itself, according to the multiplicative identity condition of 1. Hence, the following equation illustrates the multiplicative identity feature of 1.
C) 1/4 x 4 = 1
Adding 1/4 to 4 results in: 1/4 x 4 = (1 x 4) / 4 = 4/4 = 1
This demonstrates that when we multiple any number by 1, the result is always the same. Because they involve multiplying many numbers, not just 1, Options A, B, and D do not demonstrate the multiplicative identity characteristic of 1. Option C, on the other hand, multiplies one and demonstrates that the result is one, proving that one has the attribute of multiplicative identity.
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The manager of a coffee shop recorded the number of customers who put vanilla creamer or chocolate creamer in their coffee during one hour and classified them by age. The results are shown in the table. Coffee Creamer. Vanilla. Chocolate. Age 18 to 30. 2, 6. Age 31 plus. 4, 8 What percentage of these customers put chocolate creamer in their coffee during this hour?
The percentage of customers who put chocolate creamer in their coffee during the hour is 70%.
Finding the percentage of customers:To find the required percentage, find the number of customers that chose chocolate creamer and total the number of customers who came to choose the creamer in the hour.
Divide the number of customers that chose chocolate creamer by the total number of customers and multiply by 100.
Here we have
The manager of a coffee shop recorded the number of customers who put vanilla creamer or chocolate creamer in their coffee during one hour
The bale given is
Vanilla Chocolate
Age 18 - 30 2 6
Age 30 + 4 8
Here, number of customers = 2 + 4 + 6 + 8 = 20
No of customers that choose chocolate creamer = 6 + 8 = 14
The percentage of customers that put chocolate creamer
= [ 14/20 ] × 100 = 70%
Therefore,
The percentage of customers who put chocolate creamer in their coffee during the hour is 70%.
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Answer: 70%
Step-by-step explanation:
Suppose the annual interest rate is 7.5% and the interest is compounded annually. How much will an investment of $1,000 be worth after 3 years?
An investment of $1,000 at an annual interest rate of 7.5%, compounded annually, will be worth $1,232.28 after 3 years.
What is value?Value is a term used to describe the worth of something, either in terms of money, or in terms of importance or usefulness. Value can be determined in terms of the amount of money something is worth, or the level of importance or usefulness it has to someone. When something has a high value, it means that it is worth a lot of money or has a high level of importance or usefulness.
The value of an investment of $1,000 after 3 years at an annual interest rate of 7.5%, compounded annually, can be calculated using the following formula:
Future Value (FV) = Present Value (PV) × (1 + r)ⁿ
Where PV is the present value of the investment ($1,000 in this case), r is the annual interest rate (7.5%) and n is the number of years (3).
Using this formula, we can calculate the future value of the investment after 3 years as follows:
FV = $1,000 × (1 + 0.075)³
FV = $1,000 × 1.23228
FV = $1,232.28
Therefore, an investment of $1,000 at an annual interest rate of 7.5%, compounded annually, will be worth $1,232.28 after 3 years.
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I am needing some help with this
As you have two side lengths but no angle measures, the Pythagorean Theorem should be used to obtain the value of x.
Then the value of x is given as follows:
x = 36.3.
What is the Pythagorean Theorem?The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.
The parameters for this problem are given as follows:
Sides x and 19.Hypotenuse 41.Hence the value of x is obtained as follows:
x² + 19² = 41²
x = sqrt(41² - 19²)
x = 36.3.
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The interior angles of the pentagon
he has drawn are all less than 180°.
Ben attempts to express the
interior angles of his pentagon
using algebra.
His expressions are
xᵒ, (x +40)°, (2x − 30)°,
3(x - 40) and 3xº
Show that Ben is incorrect.
Input note: include the angle sum
of a pentagon, the value of x and
the size of any angles that don't
meet the criteria set out in the
question.
Ben is incorrect because…
Ben is incorrect because, all of Ben's expressions are erroneous since none of them equal the number 108 degrees. The correct equation is (n-2) x 180 / n.
What is the equation of interior angle in a regular polygon?A polygon is a geometric shape with a limited number of sides and two dimensions. The sides or edges of a polygon are formed by joining end-to-end segments of a straight line to form a closed shape. The intersection of two line segments, which results in an angle, is referred to as a vertex or corners.
The formula for calculating an interior angle in a regular polygon with n sides is (n-2) x 180 / n.
An internal angle in a pentagon has a measure of (5-2) x 180 / 5 = 108 degrees.
Substituting the angle in Ben's expression:
xᵒ + (x + 40)° + (2x - 30)° + 3(x - 40)° + 3x°
9x - 27° = 108
We observe that none of the value of x results in 108 degrees.
Hence, all of Ben's expressions are erroneous since none of them equal the number 108 degrees.
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Use the following matrices to perform the operation, if possible. (If not possible, enter IMPOSSIBLE into any cell of the matrix.) C=[5 3], [ 1 2]D=[4 8] ,[5,9] Find 4C+2D.
The final answer is:
4C+2D = [28 28]
[14 26]
To find 4C+2D, we first need to multiply the matrices C and D by their respective scalars, 4 and 2. Then, we add the resulting matrices together.
First, let's multiply matrix C by 4:
4C = 4[5 3] = [20 12]
[1 2] [ 4 8]
Next, let's multiply matrix D by 2:
2D = 2[4 8] = [ 8 16]
[5 9] [10 18]
Now, we can add the resulting matrices together:
4C+2D = [20 12] + [ 8 16] = [28 28]
[ 4 8] [10 18] [14 26]
So, the final answer is:
4C+2D = [28 28]
[14 26]
I hope this helps! Let me know if you have any further questions.
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A car tire has a diameter of 28 inches. How many revolutions does the tire make while traveling 500 feet? Round your answer to the nearest whole number.
Rounding to the nearest whole number, the tire makes 214 revolutions while traveling 500 feet.
What is Circumference?
Circumference is a term used in geometry to refer to the distance around the edge of a circle or any circular object. It is the total length of the boundary or perimeter of the circle. The circumference is determined by the diameter or radius of the circle, and it is calculated using the formula:
Circumference = π × diameter
The circumference of the tire is equal to the distance it travels in one revolution. Since the diameter of the tire is 28 inches, its radius is 14 inches. Therefore, the circumference of the tire is:
C = 2πr = 2π(14 inches) = 28π inches
To convert the distance of 500 feet to inches, we multiply by the conversion factor 12 inches/foot:
500 feet × 12 inches/foot = 6000 inches
Now we can find the number of revolutions of the tire:
number of revolutions = distance traveled / circumference of tire
number of revolutions = 6000 inches / 28π inches ≈ 214 revolutions
Therefore, rounding to the nearest whole number, the tire makes 214 revolutions while traveling 500 feet.
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A store has three sizes of cans of nuts. The large size contains 2 pounds of peanuts and 1 pound of cashews. The mammoth size contains 1 pound of walnuts, 6 pounds of peanuts, and 2 pounds of cashews. The giant size contains 1 pound of walnuts, 4 pounds of peanuts, and 2 pounds of enehews. Suppose that the store recelives be filled with the given sizes of cans? veion variables to the unknowns. Gian (G)! (b) Write oit the system of linear equane. (c) Solve the system using any method.
A store has three sizes of cans of nuts. The large size contains 2 pounds of peanuts and 1 pound of cashews. The mammoth size contains 1 pound of walnuts, 6 pounds of peanuts, and 2 pounds of cashews.
The giant size contains 1 pound of walnuts, 4 pounds of peanuts, and 2 pounds of enehews. Suppose that the store recelives be filled with the given sizes of cans?
To solve this problem, let's assign variables to the unknowns. Let G represent the number of giant cans, M represent the number of mammoth cans, and L represent the number of large cans.
We can then write out the system of linear equations:
2L + 1M + 4G = 2 lbs. of peanuts
1L + 6M + 1G = 1 lbs. of walnuts
1L + 2M + 2G = 2 lbs. of cashews
Solving this system of equations can be done with any method, such as substitution, elimination, or graphing.
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Find the missing length indicated. Leave your answer in simplest radical form.
The value of x is 9.75
What are similar triangles?Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
Therefore, the other side of the small triangle = √12²+9² = √ 144+81 = √225 = 15
15/9+x = 12/15
225 = 12(9+x)
225/12 = 9+x
18.75 = 9+x
x = 18.75 -9
x = 9.75
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how many quarts are in 1 1/2 gallon
Answer:
6
Step-by-step explanation:
[tex]1\frac{1}{2}[/tex] ÷ [tex]\frac{1}{4}[/tex] = [tex]\frac{3}{2}[/tex] ÷ [tex]\frac{1}{4}[/tex] = [tex]\frac{3}{2}[/tex] × [tex]\frac{4}{1}[/tex] = [tex]\frac{12}{2}[/tex] = 6
The LA Dodgers hit the most
homeruns in 2014. The number of
homeruns accounted for 6% of the entire
Major League Baseball homerun count. If 583
total homeruns were hit, approximately how
many did the LA Dodgers hit?
show work plsss
The number of home-runs LA Dodgers hit is 35.
What is Percentage?Percentage is a number or ratio that can be expressed as a fraction of 100.Thus y percentage of some value x is x * (y/100)Given,
Total home runs in Major league = 583
Home - runs accounted by LA Dodgers = 6 %
Number of home-runs by LA Dodgers
= 6% of 583
= 6/100 * (583)
= 0.06 * 585
= 34.98
= 35 approximately
Hence, the total number of homeruns that did the LA Dodgers hit are 35 approximately.
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Given that x = - 9 is a root of |(x,3,7)(2,x,2)(7,6,x)| = 0
x-3-7
2-x-2 = 0
7-6-x
find-the-other-roots
The other two roots are x = (9 + √137) / 2 and x = (9 - √137) / 2.
Given that x = -9 is a root of |(x,3,7)(2,x,2)(7,6,x)| = 0, we can use the determinant of the matrix to find the other roots. The determinant of the matrix is given by:
| (x,3,7)(2,x,2)(7,6,x) | = x(x*x - 2*6) - 3(2*x - 7*2) + 7(2*6 - 7*x)
= x^3 - 12x - 3(2x - 14) + 7(12 - 7x)
= x^3 - 12x - 6x + 42 + 84 - 49x
= x^3 - 67x + 126 = 0
Since x = -9 is a root, we can divide the polynomial by (x + 9) to get:
(x^3 - 67x + 126) / (x + 9) = x^2 - 9x - 14
Now we can use the quadratic formula to find the other two roots:
x = (-(-9) ± √((-9)^2 - 4(1)(-14))) / (2(1))
x = (9 ± √(81 + 56)) / 2
x = (9 ± √137) / 2
Therefore, the other two roots are x = (9 + √137) / 2 and x = (9 - √137) / 2.
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PLEASE HELP ME
Write 3 5/6 feet as a single fraction greater than one.
Then, complete the expression.
3 5/6x12
let's convert the mixed fraction to improper fraction first.
[tex]\stackrel{mixed}{3\frac{5}{6}}\implies \cfrac{3\cdot 6+5}{6}\implies \stackrel{improper}{\cfrac{23}{6}} \\\\[-0.35em] ~\dotfill\\\\ 3\frac{5}{6}\times 12\implies \cfrac{23}{6}\times 12\implies \cfrac{23}{6}\times \cfrac{12}{1}\implies \cfrac{23}{1}\times \cfrac{12}{6}\implies 23\times 2\implies \text{\LARGE 46}[/tex]
Write three rational expressions that simplify to (x)/(x+1), none of which may have a monomial in either the numerator or denominator. Show that your expressions simplify.
Three rational expressions that simplify to (x)/(x+1) are:
1) (x+2-2)/(x+1)
2) (2x-3x+3)/(2x+2-3x+1)
3) (3x+5-5-2x)/(x+2+1-2)
To simplify these expressions, we can combine like terms in the numerator and denominator:
1) (x+2-2)/(x+1) = (x)/(x+1)
2) (2x-3x+3)/(2x+2-3x+1) = (-x+3)/(-x+3) = (x)/(x+1)
3) (3x+5-5-2x)/(x+2+1-2) = (x)/(x+1)
As shown, all three expressions simplify to (x)/(x+1), fulfilling the requirements of the question.
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(Answer quick) Someone mind helping?
Answer:
x=25°
Step-by-step explanation:
please mark as brainliest
Answer:
See below.
Step-by-step explanation:
We are asked to find the value of x, and what these 2 angles are.
We know that these angles are Vertical Angles.
What are Vertical Angles?Vertical Angles are angles that are opposite of each other and are equal. They're equal due to the two straight lines crossing over each other at the same angle.
These angles aren't Adjacent Angles because they aren't next to each other. These angles don't share a common side. (Ray)
Since Vertical Angles are equal:
[tex]75 = 4x - 25[/tex]
Simplify for x:
[tex]100=4x\\25 = x[/tex]
x will equal 25°.
find the measure of ycg
Answer:
59
Step-by-step explanation:
Opposite angles are equal
C or KCG isn121
Straight line angle is 180
YCG + GCK = 180
YCG = 180- 121
Another method
All the four angles at a point is 360
YCH + HCK + KCG +YCG is 360
C is 121
121 + X + 121 + X = 360
2X + 242 =360
Subract 242 from both sides
2X = 118
Divide both sides by 2 = 59
what table models the quadratic function with a range [5, ∞]?
Answer:
It is D
Step-by-step explanation:
Its D it has to be 5 and bigger than 5
Math question 9 help
Answer:
True
Step-by-step explanation:
Plug in x = 1 into the function expression. You should get f(xx) = 4
Plug in x = 2 and you will get f(x) = 13
So the function value has increased from 4 at x = 1 to 13 at x = 2
or, just plot it and see it visually
Cool Down
1.5 Signed Numbers
Here is a set of signed numbers: 7, -3,2 -0.8, 0.8,-10-2
1. Order the numbers from least to greatest.
2. If these numbers represent temperatures in degrees C
The 15 rows of bleachers in the school gym are labeled A through O. What is the probability that a person is randomly assigned a seat in rows A,B,C, E?
The probability that a person is randomly assigned a seat in rows A,B,C, E is 4/15.
The probability that a person is randomly assigned a seat in rows A,B,C, E can be calculated by dividing the number of desired outcomes by the total number of possible outcomes.
In this case, the desired outcomes are the rows A,B,C, and E, which is a total of 4 rows. The total number of possible outcomes are the 15 rows of bleachers in the school gym, labeled A through O.
So, the probability is calculated as follows:
P(A,B,C, or E) = 4/15
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how far away is 200 m from -55 m
10 pages in 1 day = 20 pages in
days
Answer:2
Step-by-step explanation:
20 divided by 10 equals 2
Condense to a single logarithm with a leading coefficient of
1.
ln(3) + ln(x) + ln(y)
The condensed form of the given logarithmic expression ln(3) + ln(x) + ln(y) is: ln(3*x*y)
To condense the given logarithmic expression to a single logarithm with a leading coefficient of 1, we can use the product property of logarithms.
The product property states that the sum of two logarithms with the same base is equivalent to the logarithm of the product of the two numbers.
Using this property, we can combine the three logarithmic terms in the given expression: ln(3) + ln(x) + ln(y) = ln(3*x*y)
Therefore, the condensed form of the given logarithmic expression is:
ln(3*x*y). This is a single logarithm with a leading coefficient of 1, as required.
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Gary earns $9.12 per hour at his job. He worked 24 hours last week. Calculate Gary's pay before taxes.
Gary's pay before taxes is $218.88.
Gary's pay before taxes can be calculated by multiplying his hourly rate by the number of hours he worked.
Taxes are compulsory payments made by a government organisation, whether local, regional, or federal, to people or businesses. Tax revenues are used to fund a variety of government initiatives, such as Social Security and Medicare as well as public infrastructure and services like roads and schools.
Step 1: Identify the hourly rate and number of hours worked.
Hourly rate: $9.12
Hours worked: 24
Step 2: Multiply the hourly rate by the number of hours worked.
$9.12 * 24 = $218.88
Step 3: The result is Gary's pay before taxes.
Gary's pay before taxes is $218.88.
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Carys calculates the total amount E, in dollars, theat she earns for working h hours using the equation E=10h. . At that rate, how many hours does it take Carts to earn one dollar
It takes Carys 1/10 οf an hοur, οr 6 minutes, tο earn οne dοllar.
What is the linear functiοns?In mathematics, the term linear functiοn refers tο twο distinct but related nοtiοns: In calculus and related areas, a linear functiοn is a functiοn whοse graph is a straight line, that is, a pοlynοmial functiοn οf degree zerο οr οne.
Tο find the number οf hοurs it takes Carys tο earn οne dοllar, we can set E (the amοunt earned) equal tο $1 and sοlve fοr h (the number οf hοurs):
E = 10h
$1 = 10h
h = $1/10
Hence, it takes Carys 1/10 οf an hοur, οr 6 minutes, tο earn οne dοllar.
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Carys earns one dollar in one-tenth of an hour, or six minutes.
What exactly are linear functions?The word linear function in mathematics refers to two distinct but related concepts: A linear function in calculus and related fields is a function whose graph is a straight line, Namely, a polynomial function of degree zero or one.
Set E (the amount earned) to $1 and solve for h (the number of hours):
According to the given data:E = 10h
$1 = 10h
h = $1/10
As a result, it takes Carys one-tenth of an hour, or six minutes, to earn one dollar.
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Andrew had a piece of foam in the shape of a rectangular prism as shown below. Thebase is a square with sides 3 Inches long, and the piece is 5 Inches taill. He out the
foam along the diagonal plane shown by the shaded area.5 inches 3 inches Which of the following is closest to the area of the shaded diagonal plane? 19.3 square inches 12 square Inches 15.8 square inches 17.5 square inches
The area of the shaded diagonal plane is 17.5 square units.
What is the area of the shaded diagonal plane?The area of the shaded diagonal plane is calculated as follows:
Using Pythagoras' theorem, let the hypotenuse formed by the diagonal be x
x² = 3² + 5²
x² = 9 + 25
x² = 34
x = √34
The shape of the shaded plane is a rectangle.
The area of the rectangle will be:
Area = length * width
Area = √34 * 3
Area do the shaded plane = 17.5 square units
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