It will take about 11.55 years to double his money.
Important information:
Principal value = $5,000Rate of interest = 6% compounded continuously.Continuous compound interest:The formula for the amount in continuous compound interest is:
[tex]A=Pe^{rt}[/tex]
Where A is the amount, P is the principal, r is the rate of interest and t is time in years.
Substitute [tex]A=10000, P=5000,r=0.06[/tex].
[tex]10000=5000e^{0.06t}[/tex]
[tex]\dfrac{10000}{5000}=e^{0.06t}[/tex]
[tex]2=e^{0.06t}[/tex]
Taking ln on both sides, we get
[tex]\ln 2=\ln e^{0.06t}[/tex]
[tex]\ln 2=0.06t[/tex]
[tex]\dfrac{\ln 2}{0.06}=t[/tex]
[tex]t=11.55245[/tex]
[tex]t\approx 11.55[/tex]
Therefore, it will take about 11.55 years to double his money.
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John runs 15 miles in 3 hours. How many miles can John run per hour?
Answer:
5 yeet
Step-by-step explanation:
Supriya is decorating her bedroom. She plans to hang strings of twinkle lights all the way around her walls. She measures the walls and finds she will need 36 meters of lights. Which measurement did Supriya find?
Answer:
Perimeter
Step-by-step explanation:
Perimeter is the distance all round a particular shape. Since we are not given the shape of her bedroom, we may not have a particular formula that was uses to find the perimeter. Despite all that, the only way that she could arrive to conclusion that 36 meters of light are needed, then Supriya it is by finding the perimeter.
A swimming pool is to be drained. The pool is shaped like a rectangular prism with length 30 feet, wide 18 ft, and depth 4ft. Suppose water is pumped out of the pool at a rate of 216ft3 per hour. If the pool starts completely full, how many hours does it take to empty the pool?
Answer: it will take 9 hours to empty the pool.
Step-by-step explanation:
The pool is shaped like a rectangular prism with length 30 feet, wide 18 ft, and depth 4ft. It means that when the pool is full, its volume is
30 × 18 × 4 = 2160 ft³
If water is pumped out of the pool at a rate of 216ft3 per hour, then the rate at which the water in the pool is decreasing is in arithmetic progression. The formula for determining the nth term of an arithmetic sequence is expressed as
Tn = a + d(n - 1)
Where
a represents the first term of the sequence(initial amount of water in the pool when completely full).
d represents the common difference(rate at which it is being pumped out)
n represents the number of terms(hours) in the sequence.
From the information given,
a = 2160 degrees
d = - 216 ft3
Tn = 0(the final volume would be zero)
We want to determine the number of terms(hours) for which Tn would be zero. Therefore,
0 = 2160 - 216 (n - 1)
2160 = 216(n - 1) = 216n + 216
216n = 2160 - 216
216n = 1944
n = 1944/216
n = 9
Step-by-step explanation:
Answer: it will take 9 hours to empty the pool. Step-by-step explanation: The pool is shaped like a rectangular prism with length 30 feet, wide 18 ft, and depth 4ft. It means that when the pool is full, its volume is 30 x 18 x 4 = 2160 ft3 If water is pumped out of the pool at a rate of 216ft3 per hour, then the rate at which the water in the pool is decreasing is in arithmetic progression. The formula for determining the nth term of an arithmetic sequence is expressed as Tn = a + d(n - 1) Where a represents the first term of the sequence(initial amount of water in the pool when completely full). d represents the common difference(rate at which it is being pumped out) n represents the number of terms(hours) in the sequence. From the information given, a = 2160 degrees 216 ft3 d = Tn = 0(the final volume would be zero) We want to determine the number of terms(hours) for which Tn would be zero.
We want to determine the number of terms(hours) for which Tn would be zero. Therefore,
O = 2160 - 216 (n - 1) 2160 = 216(n - 1) = 216n + 216 216n = 2160 - 216 216n = 1944 %3D n = 1944/216 n = 9
what’s the answer? i really need help ???
Answer:
C, 288 square yards
Step-by-step explanation:
The first step is to find the area of the triangular base. [tex]\frac{6\cdot 8}{2}=24[/tex]. Now you can multiply by the length of the prism, 12, to find the volume. 12*24=288, or option C. Hope this helps!
Please help my grade is really low in this class
Answer:
A
Step-by-step explanation:
When completing the square, the first thing you want to do is get all of the numbers on one side, and all the x terms on the other.
Answer:
A
Step-by-step explanation:
the first thing you should do while completing the square should be moving your 'c' value to the other side of the equation!
do so by subtracting 8 on both sides,
your new equation should now look like x^2 -6x = -8
that is the first step of completing the square!
i hope this helps!!
you can totally bring your grade in math up!!
i believe in you!
stay safe!
:)
the circumference of a circle c with a radius of r units is approximately given by the linear equation C=6.3r. Find two solutions of this function. Explain the solutions.
Final answer:
The circumference of a circle with a given radius can be calculated using the linear equation C = 6.3r. Two examples of solutions to this equation are C = 12.6 units when r = 2, and C = 31.5 units when r = 5.
Explanation:
The circumference of a circle with a radius of r units is given by the linear equation C = 6.3r. To find two solutions of this function, we can substitute different values for r into the equation.
For example, if we let r = 2, then the circumference C is calculated as C = 6.3 * 2 = 12.6 units.
Another solution is when r = 5. In this case, the circumference C is C = 6.3 * 5 = 31.5 units.
A rectangle has a height of 333 and a width of 3x^2+4x3x 2 +4x3, x, squared, plus, 4, x. Express the area of the entire rectangle. Expression should be expanded.
Answer:
[tex]9x^2+12x[/tex]
Step-by-step explanation:
Height of the Rectangle =3
Width of the Rectangle =[tex]3x^2+4x[/tex]
Area of a Rectangle = Height X Width
[tex]=3(3x^2+4x)\\=9x^2+12x[/tex]
The area of the rectangle is therefore given by:
[tex]9x^2+12x[/tex]
To find the area of the rectangle, multiply its height by its width. In this case, expand the expression for the width by distributing the terms. Simplify and combine like terms to get the expanded expression for the area: 999x^4 + 36x^3 + 16x.
Explanation:To find the area of a rectangle, we multiply its length (height) by its width. In this case, the height is given as 333 and the width is given as 3x^2 + 4x3x^2 + 4x3x, x^2 + 4, x. To expand this expression and find the area, we can distribute the numbers/variables inside the parentheses.
We have (3x^2 + 4x3x^2 + 4x3x) * (x^2 + 4x). Distributing the terms inside, we get 3x^2 * x^2 + 3x^2 * 4x + 4x3x^2 * x^2 + 4x3x^2 * 4x + 4x3x * x^2 + 4x3x * 4x. Simplifying further, we have 3x^4 + 12x^3 + 4x^4 + 16x^3 + 4x^3 + 16x.
The area of the rectangle is the product of the height and width, so the expanded expression for the area is (333) * (3x^4 + 12x^3 + 4x^4 + 16x^3 + 4x^3 + 16x). Combining like terms, we have 999x^4 + 36x^3 + 16x. This is the expanded expression for the area of the rectangle.
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3x + y = -1
2x + 3y = 18
Answer: [tex]x=-3\\y=8[/tex]
Step-by-step explanation:
[tex]3x+y=-1\\2x+3y=18[/tex]
Multiply by -3 the upper equation to make y equal in value but with opposite signs.
[tex](-3)(3x+y=-1)\\-9x-3y=3[/tex]
Now add equation 1 and 2.
[tex]-9x-3y=3\\2x+3y=18[/tex]
--------------------------
[tex]-7x=21[/tex]
Solve for x;
To isolate x, divide by -7
[tex]\frac{-7x}{-7}=\frac{21}{-7}[/tex]
[tex]x=-3[/tex]
Now use one of the equations above and replace the value of x.
[tex]3x+y=-1\\3(-3)+y=-1\\-9+y=-1\\y=-1+9\\y=8[/tex]
To prove if it's correct, take either equation and replace both x and y values, if the results are equal to each other, it is correct.
[tex]2x+3y=18\\2(-3)+3(8)=18\\-6+24=18\\18=18[/tex]
UESTION 3 Researchers discovered that the curved carapace (shell) length of these turtles is approximately normally distributed with a mean of 55.7 centimeters and a standard deviation of 12 cm. The minimum and maximum size limits for captured sea turtles in the legal marine turtle fishery are 40cm and 60cm, respectively. How likely are you to capture a green sea turtle that is considered illegal?
Final answer:
The probability of capturing a green sea turtle considered illegal due to its size is about 45.52%. This is calculated using Z-scores and probabilities from the normal distribution, given the mean turtle size and standard deviation.
Explanation:
In the scenario provided, the probability of capturing a green sea turtle that is considered illegal (outside the 40cm to 60cm size limits) can be determined using normal distribution calculations. Given that the curved carapace length of these turtles is approximately normally distributed with a mean of 55.7 centimeters and a standard deviation of 12 cm, we will calculate the Z-scores for both size limits and then find the corresponding probabilities.
The Z-score formula is: Z = (X - μ)/σ, where X is the value in question, μ is the mean, and σ is the standard deviation. For the minimum size limit (40cm), Z = (40 - 55.7)/12 = -1.308. For the maximum size limit (60cm), Z = (60 - 55.7)/12 = 0.358.
Using standard normal distribution tables or a calculator, we find the probability corresponding to the Z-score of -1.308 and 0.358. The area to the left of Z = -1.308 is approximately 0.0951, and to the left of Z = 0.358 is approximately 0.6399. The probability of catching an illegal turtle is the sum of the probabilities of catching one smaller than 40cm and one larger than 60cm, which is P(X < 40) + P(X > 60) = 0.0951 + (1 - 0.6399) = 0.0951 + 0.3601 = 0.4552, or 45.52%.
Todd earned some money doing chores. He spent one-fourth of his money see a movie. Then he spent $6.00 on popcorn and drinks. When he went home, he had $24.00 left. How much did Todd earn mowing the neighbor's lawn?
Answer: Todd earned $40 mowing the neighbor's lawn.
Step-by-step explanation:
Let x represent the amount of money that Todd earned, mowing his neighbor's lawn.
He spent one-fourth of his money see a movie. It means that the amount spent in seeing a movie is x/4
Then he spent $6.00 on popcorn and drinks. It means that the total amount spent is
x/4 + 6
The amount left would be
x - (x/4 + 6) = x - x/4 - 6
When he went home, he had $24.00 left. It means that
x - x/4 - 6 = 24
x - x/4 = 24 + 6
x - x/4 = 30
Cross multiplying by 4, it becomes
4x - x = 120
3x = 120
x = 120/3
x = $40
Answer: 40$ got it right on edge :)
Step-by-step explanation:
What is the equation of the line with the same slope as the equation x-4y=3 and the y-intercept(0,-8)?
Answer:
y = 1/4x -8
Step-by-step explanation:
First find the slope of the line
x-4y =3
Subtract x from each side
x-4y -x = -x+3
-4y = -x+3
Divide each side by -4
-4y/-4 = -x/-4 +3/-4
y = 1/4 x -3/4
This is in the form y= mx+b where the slope is m and the y intercept is b
The slope is 1/4
We want the same slope
y = 1/4x +b
we know the y intercept is -8
y = 1/4x -8
One letter was selected at random from the words San Antonio. What is the probability that the selected letter was either an a or an n
The required probability of the selected letter was either an a or an n is 0.5.
Given that,
One letter was selected at random from the words San Antonio. The probability that the selected letter was either an a or an n is to be determined.
Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
Total letters = 10
Total a and n = 2 and 3
The probability is given as = 2 / 10 + 3 / 10
= 5/10 = 1/2 = 0.5
Thus, the required probability of the selected letter was either an a or an n is 0.5.
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solve the system of equations
-5x+2y=9
y=7x
Answer:
x=1, y=7
Step-by-step explanation:
-5x+2y=9
y=7x
Since you know what y is relative to x, you can plug it into the formula to find your answer.
-5x+2(7x)=9
14x-5x=9
x=1
y=7
Hope this helps!
A school chorus has 90 sixth-grade students and 75 seventh-grade students. The music director wants to make groups of performers, with the same combination of sixth- and seventh-grade students in each group. She wants to form as many groups as possible. a. What is the largest number of groups that could be formed? groups b. If that many groups are formed, how many students of each grade level would be in each group? sixth-grade students and seventh-grade students
Answer:
a) 15 is the largest number of groups that can be made.
b) There would 6 sixth grade students and 5 seventh grade students in each group.
Step-by-step explanation:
Number of sixth-grade students = 90
Number of seventh-grade students = 75
a) What is the largest number of groups that could be formed?
Since the music director wants to make groups with the same combination of sixth and seventh grade students in each group,
The greatest common factor (GCF) of the number of sixth and seventh grade students would give us the required combination.
Factor of 90 = 2*45 = 2*3*15 = 2*3*3*5
Factor of 75 = 3*25 = 3*5*5
The greatest common factors are 3 and 5
GCF = 3*5 = 15
Therefore, 15 is the largest number of groups that can be made.
b. If that many groups are formed, how many students of each grade level would be in each group?
Sixth grade = 90/15 = 6
Seventh grade = 75/15 = 5
Therefore, there would 6 sixth grade students and 5 seventh grade students in each group.
1. 15 groups. The greatest common factor of 75 and 90 is 15. 2. 6 sixth-grade students and 5 seventh-grade students
2. 6 sixth-grade students and 5 seventh-grade students ( 6 ⋅ 15 = 90 and
5 ⋅ 15 = 75 )
URGENT PLZZZ!!!! for the given situation identify the independent and dependent variables and then find a reasonable domain and range of values. Listed below will be four statements that relate to the given situation. She’s the statement that would have to be false given the situation and it’s parameters.
chain owns a scooter that can travel 65 miles per gallon of gasoline. her tank holds 2.5 gallons. She’s planning on taking a shopping trip around her city.
here are the statements
1) The range is 0 miles to 162.5 miles
2) The dependent variable is how many hours she will spend shopping in the stores
3) The independent variable is how much gasoline she’ll use
4) The domain is 2.5 gallons to 0 gallons
Answer:
2
Step-by-step explanation:
the dependent variable is the amount of time she spends driving around.
Final answer:
In the scenario, the independent variable is the amount of gasoline used, and the dependent variable is the distance traveled. The domain is 0 to 2.5 gallons and the range is 0 to 162.5 miles, hence statement 2 is false regarding the dependent variable.
Explanation:
For the given situation, the independent variable is the amount of gasoline she'll use. This is because it is the variable that can be changed freely and does not depend on the other variables in the situation. In contrast, the dependent variable is the distance that can be traveled with the scooter, as it depends on the amount of gasoline used.
The domain for this situation would be the amount of gasoline available for use, which is between 0 gallons (an empty tank) and 2.5 gallons (a full tank). The range would be the distance the scooter can travel on that gasoline, from 0 miles (no gasoline) to 162.5 miles (2.5 gallons at 65 miles per gallon).
Therefore, statement 2 "The dependent variable is how many hours she will spend shopping in the stores" would have to be false given the situation and its parameters, because the dependent variable is actually the distance that can be traveled, not the time spent shopping.
The recipe has 10 tomatoes, 6 cucumbers, and 3 peppers. What is the ratio of tomatoes to peppers?
Group of answer choices
10/3
6/3
3/6
3/10
Answer:
10/3
Step-by-step explanation:
Answer:
no of tomatoes: no of pepper
10:3
Find the area of a regular octagon with a side length of 10 cm. Round to the nearest tenth.
The question keeps telling me to STOP! Never mind.
The octagon is 8 isosceles triangles. Each has common side r and base 10. The central angle is 360/8 = 45°. By the Law of cosines,
10² = r² + r² - 2 r² cos 45° = 2r²(1 - √2/2) = r²(2-√2)
r² = 100/(2-√2)
The area of a triangle with sides a,b and included angle C is (1/2)ab sin C. Our 8 octagon isosceles triangles each have sides r and r and included angle 45° so our total area, 8 triangles, is
A = 8(1/2) r² sin 45° = (400/(2-√2)) (√2/2) × (2+√2)/(2+√2) = 200(1+√2)
A ≈482.84271
Answer: 482.8 sq cm
Final answer:
To find the area of a regular octagon with a side length of 10 cm, use the formula: Area = 2 * (1 + √2) * side length². Substitute the given side length and round the answer to the nearest tenth.
Explanation:
To find the area of a regular octagon with a side length of 10 cm, we can use the formula:
Area = 2 * (1 + √2) * side length²
Substituting the given side length into the formula:
Area = 2 * (1 + √2) * (10)²
Area = 2 * (1 + √2) * 100
Area ≈ 414.2 cm² (rounded to the nearest tenth)
After further computation, the area approximates 414.2 cm², rounded to the nearest tenth. This formula captures the geometric intricacies of a regular octagon, demonstrating a concise method to calculate its area based on the given side length. This formula encapsulates the unique characteristics of a regular octagon, providing a streamlined approach to computing its area and showcasing the elegant relationship between side length and the polygon's spatial coverage.
Which point lies on the circle represented by the equation (x + 5)2 + (-9)2 = 82?
A. (0,8)
B. (13,-9)
c. (-5,1)
D. (3,17)
Answer:
None of the given points lies on the circle.
Step-by-step explanation:
The circle is represented by the following formula:
(x - xc)² + (y - yc)² = r²
Where (xc,yc) are the coordinates of the center and r is the radius of the circle. In the case we have:
(x+5)² + (y-9)² = 82
If a point belongs to this circumference, then the results of applying the points to the equation should be valid. To test all the points we are going to apply each to the equation as shown below:
A.
(0 + 5)² + (8-9)² = 82
5² + (-1)² = 82
25 + 1 = 82
26 = 82 (invalid)
The point does not lies on the circle.
B.
(13 + 5)² + (-9-9)² = 82
(18)² + (-18)² = 82
324 + 324 = 82
648 = 82 (invalid)
The point does not lies on the circle.
C.
(-5 + 5)² + (1 - 9)² = 82
0² + (-8)² = 82
64 = 82 (invalid)
The point does not lies on the circle.
D.
(3 + 5)² + (17-9)² = 82
8² + 8² = 82
64 + 64 = 82
128 = 82 (invalid)
The point does not lies on the circle.
Answer:
c
Step-by-step explanation:
Matrix question is so confusing
(These values are the same as in the given matrix)
The bottom row's answer boxes are: 0, 1, -9/13=======================================================
Explanation:
Row echelon form will have us turn the "3" into a 0. To do this, we multiply everything in row 1 by the value -3
Row 1 is initially: 1, -4, 3
Multiply that row by -3 to get: -3, 12, -9
Then add these values to the values in row 2 and we get:
-3+3 = 0
12+1 = 13
-9+0 = -9
These three sums replace what you see in row 2
This is the new matrix we have now
[tex]\left[\begin{array}{ccc}1 & -4 & 3\\0 & 13 & -9\end{array}\right][/tex]
Again the first row has not changed. Only the second row has been altered.
The next and last step is to turn that 13 into a 1. Recall we want the pivot positions to be 1. Divide everything in row 2 by 13 to get this accomplished.
0---> 0/13 = 0
13 ----> 13/13 = 1
-9 ---> -9/13
we now have
[tex]\left[\begin{array}{ccc}1 & -4 & 3\\0 & 1 & \frac{-9}{13}\end{array}\right][/tex]
We stop here since we don't need to get the matrix into reduced row echelon form (RREF) and instead only need to get it into row echelon form (REF). Throughout this whole process, row 1 has not changed.
What are two numbers that are the same equal to 28
Answer:
2 and 14?
Step-by-step explanation:
Multiplied together they are 28, but I don't know if that's what you were asking
HURRRY PLEASE N HELP
Coach McGee uses the
table to show her team's current basketball shot average compared to previous years,
2010
2008
-5.8
2009
4.4
10
-
2012
2013
2011
3.6
Which comparison is true? Use the number line to help you.
-6 -5 -4 -3 -2 -1 0
1 2 3 4 5 6
0 -5.8>-53
Answer:
b
Step-by-step explanation:
Answer:
the answer is B
Step-by-step explanation
hope it helps!
Suppose you order an ice cream cone that holds 157 cubic centimeters of your favorite flavor. You calculate the height of your cone is 12cm. Find the diameter of your ice cream cone. (Use π≈3.14, and round to the nearest hundredth.)
Answer: Diameter = 7.06 cm
Step-by-step explanation:
The formula for determining the volume of a cone is expressed as
Volume = 1/3πr²h
Where
h represents the height of the cone
r represents the radius of the cone
π is a constant whose value is 3.14
From the information given
Volume = 157 cubic centimeters
Height = 12cm
Therefore,
157 = 1/3 × 3.14 × r² × 12
157 =12.56r²
r² = 157/12.56
r² = 12.5
Taking square root of both sides of the equation, it becomes
r = √12.5
r = 3.53 cm
Diameter = 2 × radius = 2 × 3.53
Diameter = 7.06 cm
What is the solution to the equation 2 2/5 + r = 5 2/5 ?
r = 7
r = 3
r = 3
r = 3
Answer: [tex]r=3[/tex]
Simplify both sides of the equation
[tex]r+12/5=27/5[/tex]
Subtract 12/5 from both sides
[tex]r+12/5-12/5=27/5-12/5[/tex]
[tex]r=3[/tex]
The solution to the equation 2 2/5 + r = 5 2/5 is r = 3, which is found by subtracting 2 2/5 (converted to 12/5) from 5 2/5 (converted to 27/5).
Explanation:The solution to the equation 2 2/5 + r = 5 2/5 is found by isolating the variable r.
First, convert the mixed numbers to improper fractions.
We have 12/5 (equivalent to 2 2/5) and 27/5 (equivalent to 5 2/5).
Now, subtract 12/5 from both sides of the equation to get r on one side:
27/5 - 12/5 = rAfter subtraction, we find that:
r = 15/5r = 3Thus, the solution to the equation is r = 3.
To rent a boat it costs 11$ plus an additional 10$ per hour if you have 71$ write and solve an equation to solve an equation to determine how many hours you can rent the boat
A line intersects the points (-1, 3) and
(-4, 9). What is the slope-intercept
equation for this line?
Answer:
I was able to get: y = -(6/3)x + 1
Un automóvil sale de una estación y recorre en linea recta 400 metros a la derecha , luego se devuelve 500 metros se detiene y vuelve a correr 100 metros a la derecha . De acuerdo con este recorrido el automóvil esta : A. 200 metros ala izquierda de la estación B. 100 metros a la derecha de la estación C. 50 metros a la derecha de la estación D. En la estación
1015
© 5 t-shirts and a hat costs £27.00
2 t-shirts and a hat costs £12.00.
How much does a t-shirt cost?
How much does a hat cost?
t-shirt: £
hat: £
Answer:
A shirt cost £5 while the hat cost £2.
Step-by-step explanation:
What I did was guess and check until i found the amount of each item. You can also use a table to this.
the ratio of wins to loses is 5.4 for a basketball team. if the bball team played 90 games, how many games did they win ?? show work!
Answer:
40
Step-by-step explanation:
WILL GIVE BRAINLIEST!!!
Answer:
B.
Step-by-step explanation:
Answers A, D, C dont make any sense to me
PLZZ BRAINLIEST
Consider the graphs of f(x)= sin x and g(x) = cos x. Which of the following features are the same for both graphs? Select all that apply.
Answer:
Step-by-step explanation:
All but the x- and y-intercepts are the same.
We can conclude the following similarities between the sin(x) and cos(x) -
Their amplitudes are same i.e. 1They have same domain.They have same range.They have same period of 2π.What is function?A function is a relation between a dependent and independent variable. We can write the examples of functions as -
y = f(x) = ax + b
y = f(x, y, z) = ax + by + cz
Given are the graphs of the function -
f(x) = sin(x)
g(x) = cos(x)
For the functions sin(x) and cos(x) -
Their amplitudes is same i.e. 1They have same domain.They have same range.They have same period of 2π.Therefore, we can conclude the following similarities between the sin(x) and cos(x) -
Their amplitudes are same i.e. 1They have same domain.They have same range.They have same period of 2π.To solve more questions on functions, visit the link below-
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