The rate of simple interest that Marie earns on her $800 investment is 12% per year, calculated by dividing the annual interest earned ($96) by the principal amount ($800).
To find the rate of simple interest, we can use the formula Interest = Principal * rate * time. Given that Marie earns $96 in interest each year on an investment and her principal was $800, we can rearrange the formula to solve for the rate.
The formula for simple interest is:
Interest = Principal * rate * time
Assuming the interest earned is for one year, we have:
$96 = $800 * rate * 1 year
To find the rate, we divide both sides by $800:
rate = $96 / $800
rate = 0.12
Converting into a percentage, the simple interest rate is 12% per year.
Look at the isosceles trapezoid below.
Answer:
Not enough information to decideStep-by-step explanation:
If m were the midline, its length would be 32/2 = 16 cm. However, there is nothing in the figure to indicate that is the case. There is not enough information to decide.
The area of the rectangle shown is given by the function A(x) = 2x2 - 5x. If the width of the rectangle is 13, what is the area
The area of the rectangle is 273 square units.
The task is to find the area of a rectangle where the width of the rectangle is given as 13, and the area as a function of x is provided as A(x) = 2x² - 5x.
To find the area, we need the value of x that corresponds to the width. Since the width is 13, we set x as 13 and substitute it into the area function.
A(13) = 2(13)² - 5(13) = 2(169) - 65 = 338 - 65 = 273 square units.
Thus, the area of the rectangle is 273 square units.
If f(x)=3x^2-1 and g(x)=x+2, find (f+g)(x)
Answer:
Step-by-step explanation:
X^2+3x-1 apex
An equilateral triangle has an altitude length of 36 feet. Determine the length of a side of the triangle.
dolores is selling cucumbers from her backyard garden her garden is 48 square feet in total and she can grow 1 cucumber every 72 square inches if she can successfully grow cucumbers in every square foot of the garden and sell them for $2.50 each how much will she make?
Final answer:
Dolores will make $240 by growing and selling all the cucumbers possible in her 48 square feet garden, with each cucumber selling for $2.50.
Explanation:
To calculate the amount of money Dolores will make from selling cucumbers, we need to determine how many cucumbers she can grow in her 48 square feet garden, and then multiply that number by the selling price of $2.50 per cucumber. First, we'll convert the area of her garden into square inches since we know a cucumber takes up 72 square inches of space:
48 square feet × 144 square inches per square foot = 6,912 square inches.
Next, we divide this by the amount of space needed for one cucumber to find the total number of cucumbers she can grow:
6,912 square inches ÷ 72 square inches per cucumber = 96 cucumbers.
Finally, we'll multiply the number of cucumbers by the selling price:
96 cucumbers × $2.50 per cucumber = $240.
Therefore, Dolores will make $240 by selling all the cucumbers she can grow in her garden.
Write the standard equation of a circle that passes through (1, −6) with center (7, −2).
Quadrilateral RJFT is similar to quadrilateral SYPA . JF=60 mm , AP=40 mm , and YP=25 mm . What is TF ?
Final answer:
To find the length of FT in the similar quadrilaterals RJFT and SYPA given specific side lengths, apply the scale factor method to determine FT = 37.5 mm.
Explanation:
Quadrilateral RJFT is similar to quadrilateral SYPA. Given that JF=60 mm, AP=40 mm, and YP=25 mm, we can solve for FT.
Calculate the scale factor between the two similar quadrilaterals using side lengths: JF/AP = FT/YP.
Substitute the given values to find the length of FT.
Calculate FT = (60 mm * 25 mm) / 40 mm = 37.5 mm.
Don't want any answers, just how to solve, step by step. please :)
You and a friend tutor for a total of 12 hours. Use the tape diagram to find how many hours you tutor.
I teach 9 and 6 hours respectively
Left diagram:
In this diagram you show three quarters of the hours.
We have then:
(3/4) * (12) = 9
Answer:
You teach 9 hours.
Right diagram:
In this diagram you teach half of the hours.
We have then:
(2/4) * (12) = 6
Answer:
You teach 6 hours
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You tutored for 6 hours, your friend tutored for 6 hours as well.
Image:
You and a friend listen for a total of 2 hours.
You
Friend
You
The image shows a tape diagram with two sections labeled "You" and "Friend". The "You" section is longer than the "Friend" section, indicating that you tutored for more hours than your friend.
To find the number of hours that you tutored, we can divide the total number of hours tutored (12 hours) by the number of sections in the tape diagram (2).
Number of hours you tutored = 12 hours / 2 sections = 6 hours
Therefore, you tutored for 6 hours.
Explanation of tape diagrams:
A tape diagram is a visual representation of a mathematical equation. It is a horizontal bar that is divided into sections, with each section representing a different quantity. The length of each section represents the size of the quantity it represents.
Tape diagrams can be used to solve a variety of mathematical problems, including addition, subtraction, multiplication, and division problems. They are especially useful for solving problems that involve multiple quantities, as they can help to visualize the relationships between the different quantities.
In this case, the tape diagram is used to solve the following problem:
> You and a friend tutor for a total of 12 hours. Use the tape diagram to find how many hours you tutor.
The tape diagram is divided into two sections, one for you and one for your friend. The length of each section represents the number of hours that each person tutored. Since you tutored for more hours than your friend, the "You" section is longer than the "Friend" section.
To find the number of hours that you tutored, we can divide the total number of hours tutored (12 hours) by the number of sections in the tape diagram (2). This gives us the number of hours that you tutored, which is 6 hours.
Therefore, the answer to the question is "You tutored for 6 hours."
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Consider this system of linear equations:
y = –3x + 5
y = mx + b
Which values of m and b will create a system of linear equations with no solution?
m = –3 and b = –3
m = 5 and b = –3
m = 3 and b = 5
m = 5 and b = –3
Engenuity answer is m= -3 and B= -3
m = –3 and b = –3 or A
If b is the midpoint of \frac{ }{ac} a c , d is the midpoint of \frac{ }{ce} c e , and bd = 19 , find ae .
question 1.) simplify 6(2 + 0.3)5
A.) about 0.03
B.) about 12.01
C.) about 85.19
D.) about 386.18
question 2.) solve 32x = 7
A.) x = 0.22
B.) x = 4.57
C.) x = 25
D.) x = 39
Answer: Q1) 386.18
Step-by-step explanation:
Q1): You do the parenthesis first.
6(2+0.3)^5
2+0.3 = 2.3^5 = 64.36343
then do 6(64.36343) = 386.18
For Q2 I believe the answer is 0.22 if you do 7 divided by 32 you get 0.21875 and you round that to get 0.22
helpppppppppppppppppppppppppp
Identify a possible first step using the elimination method to solve the system and then find the solution to the system.
12x – 3y = 6
2x – y = 2
A) multiply second equation by 6, solution (2,0)
B) multiply second equation by 6, solution (-2,0)
C) multiply second equation by -6, solution (0,2)
D) multiply second equation by -6, solution (0,-2)
Answer:
D) multiply second equation by -6, solution (0,-2)
Step-by-step explanation:
This pair of linear equations may be solved simultaneously by using the elimination method. This will involve ensuring that the coefficient of one of the unknown variables is the same in both equations.
As such, in the given set of equations
12x – 3y = 6
2x – y = 2
We may make the coefficients of x the same by multiplying the second by 6 or the coefficient of y by multiplying the second by 3. Using the first
12x – 3y = 6
12x – 6y = 12
equation 1 - equation 2
3y = -6
y = -2
2x + 2 = 2
x = 0
What is the measure of EG?
Use the table provided to determine the total amount paid on a 30 year fixed loan, at 6.0%, of $75,000.
$162,000
c.
$143,820
b.
$153,750
d.
$133,250
Answer:
162000
Step-by-step explanation:
For 75000 paying in 30 years at 6% we have
Mortgage Summary
Monthly Payment $449.66
Total Interest Paid $86,879
9
Total of 360 Payments $161,879
Pay-off Date Feb, 2049
We find out of 4 options given 162000 is nearer to this 161879
Hence option of 162000 is the right answer.
A doctor's office mails a survey to each of its patients. The results of the survey are based off of the total number of patients.
Which of the following could affect the outcome of their surveys?
A.The results could be flawed because the sample population was too large.
B.The results could be flawed due to a wide range of topics in the questions.
C.The survey is biased because they are only asking patients.
D.The results could be flawed due to non-response of patients.
Answer:
The results could be flawed due to non-response of patients.
Step-by-step explanation:
A doctor's office mails a survey to each of its patients. The results of the survey are based off of the total number of patients. The office is mailing the patients. It is very likely that patients do not read out the survey mail. So, they cannot respond to the survey or a very few patients will respond back. So, option 4th is the correct. The results could be flawed due to non-response of patients.
Identify the cross section shown.
a. rectangle
b. circle
c. trapezoid
d. pentagon
Option : a is the correct answer.
a. rectangle.
Step-by-step explanation:From the figure that is provided to us we see that the cross-section is in the shape of a quadrilateral such that it has two pair of parallel sides.
b)
circle
A circle does not have any edge or sides.
Hence, option: b is incorrect.
c)
Trapezoid
A trapezoid is a quadrilateral with one pair of parallel sides and one pair of unparallel sides.
Hence, option: c is incorrect.
d)
Pentagon
A pentagon is a polygon with 5 sides.
Hence, option: d is incorrect.
Hence, the best possible answer is:
Rectangle
Which of the following is false?
the number of hours a person studies and the numerical score on the exam is a positive correlation
the speed of a vehicle and the time it takes the vehicle to travel 60 miles is a positive correlation
none, since all of the other answer choices are true
a child’s age and the height of a child is a positive correlation
Answer:
the speed of a vehicle and the time it takes the vehicle to travel 60 miles is a positive correlation
given the conversion factor 3.28 ft/ 1m which cube above has the larger surface area
cube A is 7’ cube b is 2m
Final answer:
After converting Cube B's side length to feet, Cube A has a surface area of 294 ft² while Cube B has a surface area of 258.2016 ft², making Cube A the one with the larger surface area.
Explanation:
To determine which cube has the larger surface area, we must work with a common unit of measurement for both cubes. We'll convert Cube B from meters to feet using the conversion factor 3.28 ft/1m.
For Cube A with a side length of 7 feet, the surface area (SA) is calculated by the formula SA = 6 × s² (where 's' is the side length).
SA (Cube A) = 6 × (7 ft)² = 6 × 49 ft² = 294 ft².
For Cube B with a side length of 2 meters, we first convert meters to feet: 2 m × 3.28 ft/m = 6.56 ft. So, the surface area of Cube B becomes:
SA (Cube B) = 6 × (6.56 ft)² = 6 × 43.0336 ft² = 258.2016 ft².
Between Cube A and Cube B, Cube A has the larger surface area.
HELP ASAP!!
Given: ABCD is a parallelogram.
Prove: ∠A and ∠D are supplementary.
By the definition of a parallelogram, AB∥DC. AD is a transversal between these sides, so ∠A and ∠D are ? angles. Because AB and DC are ? , the same-side interior angles must be ? by the same-side interior angles theorem. Therefore, ∠A and ∠D are supplementary.
A parallelogram is a quadrilateral with four sides. The opposite sides of the parallelogram are equal and parallel.
In the given figure, AB||DC. AD is the transversal, such that:
∠A + ∠D = 180-degrees.
The parallelogram is a quadrilateral with equal and parallel sides, such that the interior angles present on the same side of the transversal are supplementary. The sum of supplementary angles is equal to 180-degrees. From the theorem of same-side interior angles, the supplementary angles present on the parallel lines must be intersected by a transversal. Since, in the parallelogram ABCD, AD is the transversal. From the property of transversal, the interior angles on the same side of the transversal are supplementary.Therefore, ∠A and ∠D are supplementary and their sum is equivalent to 180-degrees.
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WILL GIVE BRAINLIEST TO PERSON WHO ANSWERS CORRECTLY!!!!!! PLEASE HELP ASAP!!!!!
A roller coaster car follows a parabolic path over the first hill on its track. The height of the car, in feet, t seconds after the ride starts can be shown by the function given below.
h ( t ) = -3t^2 + 15t + 18
Which of the statements is true?
* The domain of the function is [0, 6], and it represents the car's time to reach maximum height.
* The domain of the function is [-1, 6], and it represents the car's time to reach maximum height.
* The domain of the function is [0, 6], and it represents the car's time to complete the hill.
* The domain of the function is [-1, 6], and it represents the car's time to complete the hill.
None of the options are entirely correct. The domain of the function is [tex]\( t \geq 0 \)[/tex] , and it does not directly represent the time to complete the hill or reach maximum height.The domain is representing all real numbers. The function doesn't directly indicate completion time or maximum height.
Let's analyze the given function [tex]\( h(t) = -3t^2 + 15t + 18 \)[/tex] to determine the domain and its meaning:
1. **Domain of the function**:
The domain of a quadratic function is all real numbers unless there are restrictions. In this case, there are no restrictions mentioned in the problem, so the domain is all real numbers. However, in the context of the roller coaster ride, the time ( t ) cannot be negative because it doesn't make sense for time to be negative in this scenario. Therefore, the practical domain is [tex]\( t \geq 0 \).[/tex]
2. **Time to reach maximum height**:
The time to reach the maximum height of the roller coaster can be found using the vertex formula: [tex]\( t = -\frac{b}{2a} \)[/tex] , where [tex]\( a = -3 \) and \( b = 15 \)[/tex] (coefficients from the quadratic function). Substituting these values into the formula:
[tex]\[ t = -\frac{15}{2(-3)} = -\frac{15}{-6} = \frac{15}{6} = \frac{5}{2} \][/tex]
Since time cannot be negative in this context, the time to reach the maximum height is [tex]\( t = \frac{5}{2} = 2.5 \)[/tex] seconds.
Now, let's analyze the given options:
- **Option 1: The domain of the function is [0, 6], and it represents the car's time to reach maximum height.**
- The domain given is correct [tex](\( t \geq 0 \)),[/tex] but it incorrectly states that it represents the time to reach maximum height. The correct time to reach maximum height is [tex]\( t = 2.5 \)[/tex] seconds, not 6 seconds.
[tex]\( t \geq 0 \),[/tex]
- **Option 2: The domain of the function is [-1, 6], and it represents the car's time to reach maximum height.**
- This option gives an incorrect domain. The domain is [tex]\( t \geq 0 \), not \( t \geq -1 \).[/tex]
- **Option 3: The domain of the function is [0, 6], and it represents the car's time to complete the hill.**
- This option correctly identifies the domain as [tex]\( t \geq 0 \).[/tex] However, it incorrectly states that it represents the time to complete the hill. The function does not directly represent the time to complete the hill; it represents the height of the car at any given time.
- **Option 4: The domain of the function is [-1, 6], and it represents the car's time to complete the hill.**
- This option gives an incorrect domain. The domain is [tex]\( t \geq 0 \),[/tex] not [tex]\( t \geq -1 \).[/tex]
Therefore, none of the options are entirely correct. The domain of the function is [tex]\( t \geq 0 \)[/tex] , and it does not directly represent the time to complete the hill or reach maximum height.
HELP FAST PLEASE!!
Martin simplified the composed function f(x)=sin(arctan x). His work is shown below.
Step 1: f(x)=sinA, where A=arctan x and x = tanA
Step 2: tanA= opp/adj=x/1
Step 3: hypotenuse= square root of 1^2-x^2= square root of 1-x^2
Step 4: sinA=opp/hyp=x/squareroot 1-x^2
In which step did Martin make is first error?
Answer:
1. B f(x)=4sinx/2-3
2. B, F, G (c=-1. a=2, b=2)
3. c. H(t)=-2.4cos(0.017t)+12
4. A, B, E, F (y=cos^-1x, y=cot^-1x, y=sin^-1x, y=tan^-1x)
5. C y=sin^-1x
6. C 48.7
7. C f(g(x))=sec(sinx) domain: all real #
8. C step 3
Step-by-step explanation:
Use the equation you have written above determine the cost for each bracelet. Show the algebraic steps that it takes to find the answer. Provide your conclusion.
One column of numbers consists of 33, 58, and 17. When the digits of the numbers are added together, the result is 3 + 3 + 5 + 8 + 1 + 7 = 27, and when the digits of 27 are then added together, the end result is 2 + 7 = 9. If the same process is performed on the numbers in a second column, what can be concluded? a.If the end result from the second column is also 9, then the sum of the numbers in the first column is equal to the sum of the numbers in the second column. b.If the end result from the second column is also 9, then the sum of the numbers in the first column is not equal to the sum of the numbers in the second column. c.If the end result from the second column is not 9, then the sum of the numbers in the first column is not equal to the sum of the numbers in the second column. d.If the end result from the second column is not 9, then the sum of the numbers in the first column is equal to the sum of the numbers in the second column.excel sum values based on another columnsum if greater than
What is the cricket’s hang time (amount of time the cricket is airborne)? Round to the nearest thousandth h(t) = –16t2 + 14t
The hang out time is 0.875 sec.
What is Quadratic equation?An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax² + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term. First, there must be a term other than zero in the coefficient of x²(a>0) for an equation to be a quadratic equation. The x² term is written first when constructing a quadratic equation in standard form, then the x term, and finally the constant term. The numerical values of a, b, and c are often expressed as integral values rather than fractions or decimals.
Given Equation:
h(t) = –16t² + 14t
For the Hangout time we can consider the function h(t)=0
0 = –16t² + 14t
16t² = 14t
16t= 14
t= 14/16
t= 0.875 sec
Hence, the hang out time is 0.875 sec.
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What is the length of a leg of an isosceles right triangle whose hypotenuse measures 6 inches? Let c represent the value of the hypotenuse. If the hypotenuse is c = a, then 6 = a. In inches, what is the value of a? 3 6
In iscosceles right triangle the value of the unknown sides is equal to [tex]3\sqrt{2}[/tex] and it can be deteremine by using pythagorean theorem.
Given :
Iscosceles right triangle.Hypotenuse = 6.Both remaining sides are equal.Let the length of unknown sides be 'a'. Than to deteremine the value of a, pythagorean theorem can be used.
[tex]\rm (Hypotenuse)^2 = (Perpendicular)^2 + (Base)^2[/tex]
[tex]6^2 = a^2+a^2[/tex]
[tex]2a^2 = 36[/tex]
[tex]a^2 =\dfrac{36}{2}[/tex]
[tex]a = \sqrt{18} =3\sqrt{2}[/tex]
Therefore, by applying pythagorean theorem the value of a which is [tex]3\sqrt{2}[/tex] can be determine.
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help help quickly!!!!!
is y=0.8(2.1)x exponential growth or exponential decay
Zack deposited $1,200 in a savings account that paid 7.75% simple
interest. What was the balance in his account at the beginning of the
third year?
a. $180
b. $270
c. $1,393.21
d. $1,470
HELPPPPP ASAP AND GET BRAINEST
Answer:
$1386.
Step-by-step explanation:
We have been given that Zack deposited $1,200 in a savings account that paid 7.75% simple interest. We are asked to find the balance in his account at the beginning of the third year.
The balance in the account at the beginning of the third year will be equal to balance in the account at the end of 2nd year.
We will use simple interest formula to solve our given problem.
[tex]A=P(1+rt)[/tex], where,
A = Amount after t years,
P = Principal amount,
r = Annual interest rate in decimal form,
t = Time in years.
Upon converting our given interest rate in decimal form we will get,
[tex]7.75\%=\frac{7.75}{100}=0.0775[/tex]
Upon substituting our given values in simple interest formula we will get,
[tex]A=\$1200(1+0.0775\cdot 2)[/tex]
[tex]A=\$1200(1+0.155)[/tex]
[tex]A=\$1200(1.155)[/tex]
[tex]A=\$1386[/tex]
Therefore, an amount of $1386 will be in Jack's account at the beginning of third year.