To find out how long it takes to earn $25 in interest on a principal of $500 at a 5% annual interest rate, use the simple interest formula. The calculation reveals it takes 1 year.
Explanation:The question asks us to determine the time it takes to earn $25 in interest on a principal of $500 at an annual interest rate of 5% using simple interest. The formula for simple interest is Interest = Principal × Rate × Time. We can rearrange this formula to solve for time (Time = Interest / (Principal × Rate)).
Given that the interest earned is $25, the principal is $500, and the rate is 5% (0.05 in decimal form), we substitute these values into our rearranged formula to find the time.
Interest = $25Principal = $500Rate = 5% or 0.05Substituting these into the formula gives us:
Time = $25 / ($500 × 0.05) = $25 / $25 = 1 year
Therefore, it takes 1 year to earn $25 in interest at a 5% annual rate on a $500 principal using simple interest.
3.) Tim is dividing up a 27 pound bag of nuts into smaller portions.
a.
How many
pound bags of nuts can be made from a 27 pound bag of nuts?
b.
How many 2 pound bags of nuts can be made from a 27 pound bag of nuts?
How many one fourths pound bags of nuts can be made from
2 and 1 half pound bag of nuts?
c.
How many three fourths pound bags of nuts can be made from a two and 1 halves pound bag of nuts?
Answer:
a=27
b=13.5
c=3.5
Step-by-step explanation:
This answer explains how to calculate the number of different sizes of bags that can be made from a specific amount of nuts, considering whole numbers of bags.
a. To determine how many 1-pound bags can be made from a 27-pound bag of nuts, divide 27 by 1, which gives you 27 bags.
b. For 2-pound bags, divide 27 by 2 to get 13.5 bags. Since you can't have half a bag, you can make only 13 bags.
c. To find the number of 3/4-pound bags from a 2.5-pound bag, divide 2.5 by 0.75, which equals 3.33 bags, but you can make only 3 bags because you can't have a fraction of a bag.
Pls find the zeros
in 10th level
Answer:
x = - 3[tex]\sqrt{2}[/tex], x = [tex]\sqrt{2}[/tex]
Step-by-step explanation:
Given
x² + 2[tex]\sqrt{2}[/tex] x - 6
To calculate the zeros equate to zero
x² + 2[tex]\sqrt{2}[/tex] x - 6 = 0 ( add 6 to both sides )
x² + 2[tex]\sqrt{2}[/tex] x = 6
One way is to use the completing the square method
add ( half the coefficient of the x- term )² to both sides
x² + 2[tex]\sqrt{2}[/tex] x + ([tex]\sqrt{2}[/tex])² = 6 + ([tex]\sqrt{2}[/tex])²
x² + 2[tex]\sqrt{2}[/tex] x + 2 = 6 + 2
(x + [tex]\sqrt{2}[/tex] )² = 8
Take the square root of both sides
x + [tex]\sqrt{2}[/tex] = ± [tex]\sqrt{8}[/tex] = ± 2[tex]\sqrt{2}[/tex]
subtract [tex]\sqrt{2}[/tex] from both sides
x = - [tex]\sqrt{2}[/tex] ± 2[tex]\sqrt{2}[/tex]
x = - [tex]\sqrt{2}[/tex] - 2[tex]\sqrt{2}[/tex] = - 3[tex]\sqrt{2}[/tex], or
x = - [tex]\sqrt{2}[/tex] + 2[tex]\sqrt{2}[/tex] = [tex]\sqrt{2}[/tex]
Out of 2 9 15 21 is not a composite
Answer:
2
Step-by-step explanation:
2 is actually a prime number because composite numbers have more than 2 factors but prime numbers don't.
Hello! I would appreciate the help, and please write step by step solutions. Will mark brainliest. Thanks!
QUESTION 5
The side length of the first tra-pezoid and the second tra-pezoid are in the ratio [tex]5:7[/tex].
To find the corresponding ratio of their area, we square each term in the ratio.
The ratio of the area of the first figure, to the ratio of the area of the second is
[tex]5^2:7^2=25:49[/tex]
QUESTION 6
The side length of the first figure and the second figure are in the ratio [tex]12:7[/tex].
To find the corresponding ratio of their area, we square each term in the ratio.
The ratio of the area of the first figure, to the ratio of the area of the second figure is
[tex]12^2:7^2=144:49[/tex]
QUESTION 7
Let [tex]h[/tex] represent the height of this triangle.
[tex]\sin 30\degree=\frac{h}{6}[/tex]
This implies that;
[tex]h=6\sin 30\degree[/tex]
[tex]h=3ft[/tex]
The area of the triangle is [tex]=\frac{1}{2}bh[/tex]
The base is 9 ft and the height is 3 ft.
We substitute these values to obtain;
[tex]A=\frac{1}{2}(9)(3)[/tex]
[tex]A=13.5ft^2[/tex] to the nearest tenth.
QUESTION 8
The area of a parallelogram is [tex]base\times\:height[/tex]
Let h represent the height of this parallelogram.
[tex]\sin60\degree=\frac{h}{6}[/tex]
[tex]h=6\sin60\degree[/tex]
[tex]h=3\sqrt{3}m[/tex]
The area of the parallelogram is [tex]=10\times3\sqrt{3}m^2[/tex]
[tex]=30\sqrt{3}m^2[/tex]
[tex]=52.0m^2[/tex] to the nearest tenth.
Which number line shows the solution set for |y-9| <12
Answer:
Option c
[tex]y\geq-3[/tex] or [tex]y \leq 21[/tex]
Step-by-step explanation:
The absolute value is a function that transforms any value x into a positive number.
Therefore, for the function [tex]f(x) = |x|[/tex] x> 0 for all real numbers.
Then the inequation:
[tex]|y-9| \leq 12[/tex] has two cases
[tex](y-9)[/tex] if [tex]y \geq 9[/tex] (i)
[tex]-(y-9)[/tex] if [tex]y < 9[/tex] (ii)
We solve the case (i)
[tex]y \leq 9 + 12\\y\leq21[/tex]
We solve the case (ii)
[tex]-y +9 \leq 12\\-y \leq 12-9\\y \geq -3[/tex]
Then the solution is:
[tex]y\geq-3[/tex] or [tex]y \leq 21[/tex]
Answer:
its c the answer above me is correct
Step-by-step explanation:
An artist has prepares a canvas on a rectangular frame that is 30 inches by 40 inches. What is the area, in square inches, of the canvas?
the answer is since A = l × w
A= 30 × 40
A= 1200 square inches
Abdul invests $5,000 at an interest
rate of 4%, compounded quarterly.
How much is the investment worth
at the end of 3 years?
Answer:
about $5,203.02
Step-by-step explanation:
5000(1+(.04/4))^4
The total amount accrued, principal plus interest, with compound interest on a principal of $5,000.00 at a rate of 4% per year compounded 1 times per year over 3 years is $5,624.32.
Given Data
Principal = $5000Rate = 4%Time = 3 yearsA = P + I where
P (principal) = $5,000.00
I (interest) = $624.32
Calculation Steps:
First, convert R as a percent to r as a decimal
r = R/100
r = 4/100
r = 0.04 rate per year,
Then solve the equation for A
A = P(1 + r/n)^nt
A = 5,000.00(1 + 0.04/1)^(1)(3)
A = 5,000.00(1 + 0.04)^(3)
A = $5,624.32
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Which of the following could be the side lengths of a triangle?
A. 12,15,30
B. 14,16,34
C. 15,16,33
D. 17, 18, 32
Here is your answer
D. 17, 18, 32
REASON:
Sum of any two sides of a triangle is always greater than the third side.
So,
17+18= 35
35>32
In other cases
a. 12+15= 27
27 <30
b. 14+16= 30
30 <34
c. 15+16= 31
31 <33
Hence other three can't be sides of a triangle.
HOPE IT IS USEFUL
The side lengths that could represent a triangle is 17, 18, 32
What is a triangle?
A triangle is a polygon with three sides and three angles. Type of triangles are isosceles, equilateral, scalene and obtuse.
For a triangle, the sum of any two sides must be greater than the third side. Hence:
For 12, 15 , 30; 12 + 15 < 30
For 14, 16 , 34; 14 + 16 < 34
For 15, 16 , 33; 15 + 16 < 33
For 17, 18 , 33; 17 + 18 > 33
The side lengths that could represent a triangle is 17, 18, 32
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Annabel uses 5 gallons of gas to drive 140 miles on the highway if she travels at the same rate how many miles can she drive on 7 gallon of gas
Answer:
196
Step-by-step explanation:
Divide 140 by 5 to find out how many miles she can drive with one gallon:
140/5 = 28
Multiply by 7:
28 x 7 = 196
hope this helps
Evaluate 10 sigma n=2 -2n-3
Answer:
-135
Step-by-step explanation:
The summation notation of 10∑n=2 -2n-3.
We can find the values by substituting n into -2n-3.
Let's begin where n = 2
-2(2) - 3 = -7
-2(3) - 3 = -9
-2(4) - 3 = -11
-2(5) - 3 = -13
-2(6) - 3 = -15
-2(7) - 3 = -17
-2(8) - 3 = -19
-2(9) - 3 = -21
-2(10) - 3 = -23
This gives us:
-7 + -9 + -11 + -13 + -15 + -17 + -19 + -21 + -23 = -135
The question is likely related to evaluating a summation sequence using sigma notation, but the specifics are unclear due to possible typos. The correct approach would be to substitute values of n into the given expression and sum the results, but the question needs clarification.
Explanation:The student's question appears to involve the concept of a summation, indicated by the sigma notation (Σ), which is a common topic in high school mathematics, particularly in algebra, pre-calculus, or AP statistics. However, the question, as written, is incomplete or contains typos that make it unclear. The phrase '10 sigma n=2 -2n-3' is not sufficient to provide a full context for an evaluation. It is likely that the student is asking to evaluate a summation formula that starts at n=2, but the upper limit of the summation (10) and the actual expression to be summed (-2n-3) are not clearly linked.
If the student intended to ask for the evaluation of the summation of the expression -2n-3 from n=2 to n=10, then we would calculate the sum as follows:
Substitute each integer value for n from 2 to 10 into the expression -2n-3.Calculate each term individually.Sum all the evaluated terms to get the final answer.However, without clarification from the student, we cannot proceed with certainty. It is important to understand the exact parameters of the summation when dealing with sigma notation and summation formulas.
A tissue box is in the shape of a rectangular prism with an area of 528 cubic inches. The length of the box of tissues is 12 inches and the height is 5 1/2 inches. What is the width of the box of tissues?
Pls help will mark the brainiest!!
The answer would be 8 inches.
Answer:
W = 8 inches
Step-by-step explanation:
Volume of a rectangular prism is V= LWH,
we are given V = 528, L = 12, and H = 5 1/2. Plug them in and find W..
First convert 5 1/2 to an improper fraction
5 1/2 becomes 11/2
528 = (12)(11/2)W
528 = (132/2)W
528 = 66W
8 = W (divide both sides by 66)
A circular plate has circumference 16.3 inches. What is the area of this plate? Use 3.14 for pi. Round to the nearest whole number as needed
Answer:
The area of the plate is 21 inches
Step-by-step explanation:
* Lets revise some rules of a circle
- The circumference of a circle = 2πr , where r is the radius of it
- The area of the circle = πr²
* Lets solve the problem
∵ A circular plate has circumference 16.3 inches
∵ The circumference = 2πr
∵ π = 3.14
- Lets find the radius of the plate
∵ 16.3 = 2(3.14)r
∴ 16.3 = 6.28r
- Divide both sides by 6.28
∴ r = 16.3/6.28 = 2.5955 ≅ 2.6
∴ The radius of the plate is 2.6 inches
* Lets find the area of the plate
∵ The area = πr²
∵ π = 3.14
∵ 4 = 2.6
∴ The area = 3.14(2.6)² = 21.22 ≅ 21
* The area of the plate is 21 inches
To find the area of a circle with a circumference of 16.3 inches using 3.14 for pi, you first calculate the radius and then use the formula A = πr² to get the area, which when rounded to the nearest whole number is approximately 21 inches².
Explanation:To calculate the area of a circular plate when given its circumference, we first need to find the radius of the circle. We use the formula for the circumference of a circle, C = 2πr, where C is the circumference, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius. The student has provided the circumference as 16.3 inches, so we solve for r:
C = 2πr
16.3 inches = 2 × 3.14 × r
16.3 inches / (2 × 3.14) = r
16.3 inches / 6.28 = r
2.597 inches = r
Now that we have the radius, we can use the area formula for a circle, A = πr². Plugging in our radius we get:
A = 3.14 × (2.597 inches)²
A = 3.14 × 6.7473 inches²
A = 21.205 inches²
Rounding to the nearest whole number:
A ≈ 21 inches²
#6. Find the area of a triangle. Thanks.
Answer:
A
Step-by-step explanation:
The area (A) is calculated using
A = [tex]\frac{1}{2}[/tex] bc sinA ← substitute values
A = 0.5 × 14 × 8 × sin30° = 28 units² → A
You read online that a 15 ft by 20 ft brick patio would cost about $2,275 to have professionally installed. Estimate the cost of having a 17 by 22 ft brick patio installed.
Answer:
15' x 20' = 300 square foot
2,275 x 300 = 7.583
17 x 22 = 374
374 x 7.583 = 2,836.042
Which you have to round to the nearest dollar
2,836.042 which will come out to be $2,837.00
Step-by-step explanation:
Find the next three terms in each sequence
Answer:
10) 40,80,160
11) 64, 256, 1024
12) 5, 2.5, 1.25
Step-by-step explanation:
Hope this helps. :)
10 points! What is answer
Answer:
B
Step-by-step explanation:
Using the rule of exponents
[tex]\frac{a^{m} }{a^{n} }[/tex] ⇔ [tex]a^{(m-n)}[/tex]
Hence
[tex]\frac{3^{4} }{3^{2} }[/tex] = [tex]3^{(4-2)}[/tex] = 3² = 9 → B
The answer is 9
because 3 to the power of 4 is 81 and 3 to the power of 2 is 9 so it’s 81 divided by 9 which is 9
Which number is the closest approximation to the value of the square root of 167
Answer:
13.
Step-by-step explanation:
12.9 is closer to 13.
square root 167 is 12.923, this rounded to the nearest unit is 13
What is a way to write 1,00,000 using exponents
Answer:
10^5
Step-by-step explanation:
100,000
= 10 x 10 x 10 x 10 x 10
= 10^5
(V2.00)
Rewrite f(x) = -2(x - 3)2 + 2 from vertex form to standard form.
Answer:
The standard form of the quadratic equation is [tex]f(x)=-2x^{2}+12x-16[/tex]
Step-by-step explanation:
we know that
The standard form of a quadratic equation is
[tex]f(x)=ax^{2}+bx+c[/tex]
we have
[tex]f(x)=-2(x-3)^{2}+2[/tex]
convert to standard form
[tex]f(x)=-2(x-3)^{2}+2\\f(x)=-2(x^{2} -6x+9)+2\\f(x)=-2x^{2}+12x-18+2\\f(x)=-2x^{2}+12x-16[/tex]
Two numbers are in ratio of 3 : 4.If their sum is 133 ,find the number. Help
Let the two numbers be 3x and 4x
sum =3x + 4x = 7x
7x = 133
x= 19
the numbers are :
3(19) = 57
4(19) = 76
Answer:
57 and 76
Step-by-step explanation:
Given the ratios are 3 : 4 = 3x : 4x, then
3x + 4x = 133
7x = 133 ( divide both sides by 7 )
x = 19
The numbers are
3 × 19 = 57 and 4 × 19 = 76
Which of the following does not belong to the solution set of -3x + 7 < 11? 4 -1 -5 0
Answer:
-5
Step-by-step explanation:
We can just see what x has to be smaller than (or plug in the numbers, but that is more time-consuming).
-3x + 7 < 11 -> -3x < 4 -> x > -4/3
-5 is the only number that is less than or equal to -4/3.
-5 Is not a solution to the inequality
Point A is located at (7, -1). After it is translated, point A' is located at (0, -1). What was the translation?
7 units to the right
7 units to the left
7 units up
7 units down
Answer:
7 units to the left
Step-by-step explanation:
Because if you move to the left you subtract 7 from the x-axis number or in this case 7, so 7-7=0.
Answer:
7 units to the left.
Step-by-step explanation:
HERE ARE TWO NUMBER MACHINES A AND B
BOTH MACHINES HAVE THE SAME INPUT X
WORK OUT THE INPUT THAT MAKES THE OUPUT OF A 3 TIMES THE OUTPUT OF B
A) input: X → times 5 → -4 output:
B) input: X → times 3 → +8 output:
Answer:
[tex]x=-7[/tex]
Step-by-step explanation:
We can write them both like functions like this
[tex]A=5x-4[/tex]
[tex]B=3x+8[/tex]
Where
x=input
A=Output A
B=Output B
We want the output of A 3 times the output of B this can be written like this:
[tex]A=3B[/tex]
we replace with the functions
[tex]5x-4=3(3x+8)[/tex]
we solve for x
[tex]5x-4=9x+24\\5x-9x=24+4\\-4x=28\\x=\frac{28}{-4}\\x=-7[/tex]
The output that makes the out put of A 3 times teh output of B is [tex]-7[/tex]
To find the input that makes the output of A three times the output of B, solve the equation 3(B's output) = A's output by plugging in the values for each machine. The input that satisfies this equation is X = -7.
Explanation:To find the input that makes the output of A three times the output of B, we need to solve the equation 3(B's output) = A's output. Let's plug in the given values into the machines to solve for X:
A machine:Input: XTimes 5Output: 5XMinus 4Final Output: 5X - 4B machine:Input: XTimes 3Output: 3XAdd 8Final Output: 3X + 8Now we can set up the equation and solve for X:
3(3X + 8) = 5X - 4
9X + 24 = 5X - 4
9X - 5X = -4 - 24
4X = -28
X = -7
Therefore, the input that makes the output of A three times the output of B is X = -7.
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Lines b and c are parallel.
Which of the following angles are congruent to ∠4? Select all that apply.
1
7
8
2
Answer:
1 and 8 are the ones you should choose.
Step-by-step explanation:
Answer: ∠1 and ∠8
Step-by-step explanation:
Given : Line b is parallel to line c .
In the given figure , a traversal line is passing through line b and c.
∠2=120°
Then , ∠1 +∠2=180° [linear pair]
⇒ ∠1=180°-120°=60°
Now, ∠4 and ∠1 are vertical angles.
Since vertical angles are congruent.
∴ we have , ∠4 ≅ ∠1 =60°
Also, ∠4 and ∠8 are corresponding angles and corresponding angles are congruent.
∴ we have , ∠4 ≅ 8 =60°
∠2 cannot be congruent to ∠4, since both have different measures
∠7 cannot be congruent to ∠4, since ∠7 is congruent to ∠2 (Alternate exterior angles)
Which represents the solution(s) of the graphed system of equations, y = x2 – 2x and y = –2x – 1? (1, –1) (0, 0) and (0, –1) (0, 0) and (2, 0) no solutions Mark this and return
ANSWER
No solution
EXPLANATION
The first equation is
[tex]y = {x}^{2} - 2x[/tex]
and the second equation is
[tex]y = - 2x - 1[/tex]
We equate the two equations to obtain;
[tex] {x}^{2} - 2x = - 2x - 1[/tex]
This implies that
[tex] {x}^{2} = - 2x + 2x - 1[/tex]
[tex] {x}^{2} = - 1[/tex]
There is no real number whose square is -1.
Therefore, the equation has no solution.
Answer: no solution
Step-by-step explanation: no cap
which polynomial is represented by the algebra tiles?
A.
[tex]2x^{2} - \: 4x \: - \: 6[/tex]
B.
[tex] {2x}^{2} + 4x + 6[/tex]
C.
[tex] -2x^{2} - 4x - 6[/tex]
D.
[tex] -2x^{2} + 4x + 6[/tex]
Answer:
2x^2-4x-6
Step-by-step explanation:
I don't know what kind of math this is, but simply add up all of the like-terms.
There are 2 +x^2 --> 2x^2
There are 4 -x --> -4x
There are 6 - --> -6
The answer is A
There are two x squared tiles, there are four negative x tiles and there are six single negative tiles
Which graph represents an odd function?
The graphs are in pictures
Answer:
B
Step-by-step explanation:
did it on edge
2 cars are driving in a highway.car A starts 10 miles ahead of car B.Car A is driving at a speed of 55 miles per hour.car B is driving at a speed of 60 miles per hour.After how Many hours will the 2 cars be in the same location?how far will car B have driven when the 2 cars leer?
Answer:
Step-by-step explanation:
60 - 55 = 5, car B catches up to Car A 5 miles per hour, they are 5 miles closer every hour
10 / 5 = 2, 2 hours
car b would have driven 60 * 2 = 120
Which of the following relations is a function click on the graph until the correct graph appears
only the last one since the others don’t pass the vertical line test
which is when you draw a straight line down your function and if it hits 2 or more points it is not a function
The correct graph should have x values that have no more than one y value.
What is function graph ?The collection of all points in the plane with the form (x, f(x)) that make up a function f's graph. We may alternatively say that the graph of f is the graph of y = f. (x). As a result, the graph of an equation is a particular instance of the graph of a function.Type of function graph ?
Depending on the kind of function that is graphed, various graph types exist.
Linear, power, quadratic, polynomial, rational, exponential, logarithmic, and sinusoidal graphs are the eight most often used types.
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-5/7 x 1/5
plz help me
Answer:
-5/7 x 1/5 = -5/35 = -7
The answers is -1/7
Hope it helped!!