Step-by-step explanation:
volume of a cylinder is pi × r² × height
r = 2.5
height= 4
volume = pi × 2.5² × 4
volume = 25 pi
AH = Actual Hours SH = Standard Hours AR = Actual Rate SR = Standard Rate Compute the direct labor rate and efficiency variances for the period and classify each as favorable, unfavorable or no variance
To compute the direct labor rate and efficiency variances, we will use the given terms: Actual Hours (AH), Standard Hours (SH), Actual Rate (AR), and Standard Rate (SR). Here's a step-by-step explanation:
Step 1: Calculate the Actual Labor Cost
Actual Labor Cost = AH * AR
Step 2: Calculate the Standard Labor Cost
Standard Labor Cost = SH * SR
Step 3: Calculate the Labor Rate Variance
Labor Rate Variance = (AR - SR) * AH
Step 4: Classify the Labor Rate Variance
If the Labor Rate Variance is positive, it is unfavorable. If it is negative, it is favorable. If it is zero, there is no variance.
Step 5: Calculate the Standard Labor Cost for Actual Hours
Standard Labor Cost for Actual Hours = AH * SR
Step 6: Calculate the Labor Efficiency Variance
Labor Efficiency Variance = (AH - SH) * SR
Step 7: Classify the Labor Efficiency Variance
If the Labor Efficiency Variance is positive, it is unfavorable. If it is negative, it is favorable. If it is zero, there is no variance.
By following these steps, you can compute the direct labor rate and efficiency variances for the period and classify each as favorable, unfavorable, or no variance.
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A credit card had a APR of 33. 01% all of last year and compounded interest daily. What was the credit card’s effective interest rate last year?
The credit card's effective interest rate for the year is [tex]40.51%.[/tex]%
To solve this problemWe can use the following formula:
Effective annual interest rate is calculated as[tex](1 + APR/365)365 - 1.[/tex]
The interest is compounded everyday in this case and the APR is 33.01 percent. When we enter these values into the formula, we obtain:
Effective annual interest rate =[tex](1 + 0.3301/365)^365 - 1[/tex]
Effective annual interest rate =[tex]1.4051 - 1[/tex]
Effective annual interest rate =[tex]1.4051 - 1[/tex]
So the credit card's effective interest rate for the year is[tex]40.51%.[/tex]%
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Which of the following is an even function? g(x) = (x – 1)2 1 g(x) = 2x2 1 g(x) = 4x 2 g(x) = 2x
The only even function among the given options is g(x) = 2x^2, so the answer is B) g(x) = 2x^2.
A function is even if it satisfies the property g(-x) = g(x) for all x.
Checking each of the given functions:
g(x) = (x - 1)^2 is not even, because g(-x) = (-x - 1)^2 = x^2 + 2x + 1, which is not equal to g(x) = (x - 1)^2.
g(x) = 2x^2 is even, because g(-x) = 2(-x)^2 = 2x^2 = g(x) for all x.
g(x) = 4x^2 is even, because g(-x) = 4(-x)^2 = 4x^2 = g(x) for all x.
g(x) = 2x is odd, because g(-x) = 2(-x) = -2x = -g(x) for all x.
Therefore, the only even function among the given options is g(x) = 2x^2, so the answer is B) g(x) = 2x^2.
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The function f(x) = 2x + 7x{-1} has one local minimum and one local maximum. This function has a local maximum at x = with value and a local minimum at x = with value
The function has a local maximum at x = -√(2/7) with value -3√14 and a local minimum at x = √(2/7) with value 3√14.
To find the local maximum and minimum of the function f(x) = 2x + 7x⁻¹, we need to find the critical points of the function and then use the second derivative test to determine if they are local maxima or minima.
First, we find the derivative of f(x):
f'(x) = 2 - 7x⁻²
Setting f'(x) = 0, we get:
2 - 7x⁻² = 0
Solving for x, we get:
x = ±√(2/7)
Next, we compute the second derivative of f(x):
f''(x) = 14x⁻³
At x = ±√(2/7), we have:
f''(±√(2/7)) = ±∞
Since f''(±√(2/7)) has opposite signs at the critical points, ±√(2/7), we conclude that f(x) has a local maximum at x = -√(2/7) and a local minimum at x = √(2/7).
To find the values of the local maximum and minimum, we plug them into the original function:
f(-√(2/7)) = 2(-√(2/7)) + 7/(-√(2/7)) = -3√14
f(√(2/7)) = 2(√(2/7)) + 7/(√(2/7)) = 3√14
Therefore, the function has a local maximum at x = -√(2/7) with value -3√14 and a local minimum at x = √(2/7) with value 3√14.
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Let S be the part of the plane 3+ + 2) + z = 1 which lies in the first octant, oriented upward. Use the Stokes theorem to find the flux of the vector field F = 3i+3j + 4k across the surface S.
The surface integral of the dot product between the vector field F = 3i + 3j + 4k and the unit normal vector of the surface S is equal to zero.
To use Stokes' theorem to find the flux of the vector field F = 3i + 3j + 4k across the surface S, which is the part of the plane 3x + 2y + z = 1 in the first octant and oriented upward.
Stoke's theorem statement is “the surface integral of the curl of a function over the surface bounded by a closed surface will be equal to the line integral of the particular vector function around it.” Stokes theorem gives a relation between line integrals and surface integrals.
First, we need to parametirize the curve C that bounds the surface S. Since S is in the first octant, x, y, and z are all non-negative.
The boundary C consists of three line segments: (i) from (0, 0, 0) to (1/3, 0, 0), (ii) from (1/3, 0, 0) to (0, 1/2, 0), and (iii) from (0, 1/2, 0) to (0, 0, 0). Next, calculate the curl of F, which is the cross product of the del operator and F:
curl(F) = (∂Fz/∂y - ∂Fy/∂z)i - (∂Fx/∂z - ∂Fz/∂x)j + (∂Fy/∂x - ∂Fx/∂y)k = (0 - 0)i - (0 - 0)j + (0 - 0)k = 0.
Since curl(F) = 0, the line integral of F over C is also 0.
According to Stokes' theorem, the flux of F across S equals the line integral of F over C, which we found to be 0.
Therefore, the flux of the vector field F = 3i + 3j + 4k across the surface S is 0.
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On a baseball diamond, home plate and second base lie on the perpendicular bisector of the line segment that joins first and third base. First base is 90 feet from home plate. How far is it from third base to home plate? Sketch a baseball diamond on a separate sheet of paper, labeling home plate as point A
, first base as B
, second base as C
, and third base as D. Label the intersection of AC⎯⎯⎯⎯⎯
and BD⎯⎯⎯⎯⎯
as E. Using the Perpendicular Bisector Theorem, determine how far it is from third base to home plate. Describe your conclusion in the context of the situation
Using the Perpendicular Bisector Theorem, the distance from third base to home plate is 90 feet. This means that all the bases are equidistant from home plate, which is a fundamental property of a baseball diamond.
To find the distance from third base to home plate, we need to use the Perpendicular Bisector Theorem, which states that if a point lies on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
First, we draw a baseball diamond with points A, B, C, and D labeled as described in the problem.
Next, we draw the line segment that joins first base (B) and third base (D), and we construct the perpendicular bisector of this segment by drawing a line through the midpoint of BD and perpendicular to BD. Let's label the point where the perpendicular bisector intersects the line that connects home plate (A) and second base (C) as E.
Since E lies on the perpendicular bisector of BD, it is equidistant from B and D. We know that first base (B) is 90 feet from home plate (A), so the distance from home plate to E must also be 90 feet. Therefore, the distance from third base (D) to home plate (A) is also 90 feet.
In conclusion, using the Perpendicular Bisector Theorem, we determined that the distance from third base to home plate is 90 feet.
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A cylindrical jar of peanut butter has a height of 4 inches and a diameter of 3 inches. How many cubic inches of peanut butter can the jar hold? Use π = 3.14.
28.26 in3
37.68 in3
113.04 in3
150.72 in3
The jar can hold 28.26 cubic inches of peanut butter
How to calculate the amount of cubic inches of peanut butter?The first step is to write out the parameters
A cylindrical jar of peanut has a height of 4 inches
The diameter is 3 inches
The next step is to calculate the radius, this is done by dividing the diameter by 2
radius= 3/2
= 1.5
The formula used to calculate the cubic inches of peanut butter is
V= πr²h
= 3.14 × 1.5² × 4
= 3.14 × 2.25 × 4
= 28.26
Hence the jar can hold 28.26 cubic inches of peanut butter
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On Friday, Jacob planted a pinto bean in science class. When he returned to school on Monday, the bean had sprouted a stem that was 3 millimeters long. At the end of the week, Jacob's bean sprout had a stem that was 42 millimeters long. How many centimeters did Jacob's bean sprout grow during the week?
Jacob's bean sprout grew 3.9 centimeters during the week.
What is measurements?
Measurements in math involve the assignment of numerical values to physical quantities, such as length, area, volume, mass, time, temperature, and so on. Measuring objects or events allows us to compare and quantify them, and is an essential part of mathematical problem-solving, as well as many other fields of study
Jacob's bean sprout grew 42 millimeters - 3 millimeters = 39 millimeters during the week.
To convert millimeters to centimeters, we need to divide by 10 since there are 10 millimeters in 1 centimeter.
So, the growth in centimeters is 39 millimeters ÷ 10 = 3.9 centimeters.
Therefore, Jacob's bean sprout grew 3.9 centimeters during the week.
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Find the slope of the line
Answer:
m = -2
Step-by-step explanation:
We Know
Slope = rise/run or (y2 - y1) / (x2 - x1)
Pick 2 points (-3,2) (-2,0)
We see the y decrease by 2, and the x increase by 1, so the slope is
m = -2
Ralph's t-shirt company sells custom t-short for $5. 00 each plus a $20 shipping and design fee. Frank's t-shirt company sells t-shirts for $10 each with no additional fees
To compare Ralph's and Frank's t-shirt companies, let's calculate the total cost of buying a certain number of t-shirts from each company.
1. Ralph's t-shirt company:
- Price per t-shirt: $5.00
- Shipping and design fee: $20.00
Total cost for Ralph's t-shirts = (number of t-shirts * $5.00) + $20.00
2. Frank's t-shirt company:
- Price per t-shirt: $10.00
- No additional fees
Total cost for Frank's t-shirts = number of t-shirts * $10.00
Now you can compare the total costs for each company depending on the number of t-shirts you want to buy.
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Lucinda has already earned $30 walking dogs. She earns $3 per dog walked, and she needs at least $80 to buy more leashes. Write and solve an inequality to determine how many more dogs Lucinda will need to walk to have at least $80.
I would say she has to walk 17 dogs, im not sure if that's correct though
Let's assume that Lucinda needs to walk "x" more dogs to have at least $80. Then, the amount of money she will earn from walking those "x" dogs can be calculated by multiplying the number of dogs by the amount of money earned per dog, which is $3:
Amount of money earned from walking "x" dogs = $3x
To determine how many more dogs Lucinda needs to walk to have at least $80, we can write the following inequality:
$30 + $3x ≥ $80
Simplifying the inequality, we get:
$3x ≥ $50
Dividing both sides by 3, we get:
x ≥ 16.67
Since we can't walk a fraction of a dog, we need to round up to the nearest whole number. Therefore, Lucinda needs to walk at least 17 more dogs to have at least $80.
PLEASE HELP WILL GIVE BRAINLEST !!!!
A magazine listed the number of calories and sodium content (in milligrams) for 13 brands of hot dogs. Examine the association, assuming that the data satisfy the conditions for inference. Complete parts a and b
Option B is correct. In this context, the meaning is: Among hot dogs with the same number of calories, the sodium content varies, with a standard deviation of about 75 milligrams
The calculated test statistic is 3.75
How to get the correct optionThe test statistics can be gotten from the data that we already have available in this question
The coefficient is given as 2.235
The Standard error of the coefficient is given as 0.596
The formula used is given as
Such that t = coefficient / Standard error
where the coefficient = 2.235
The standard error = 0.596
We have to apply the values to formula:
= 2.235 / 0.596
= 3.75
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PLease help 1 and 2 Pythagorean Theorem and if you can explain please
Answer:
Step-by-step explanation:
The Pythagorean theorem has the formula a squared(leg) + b squared(leg) = c squared(longest leg). This means [tex]12^{2} +16^{2} =20^{2} -- > 144+256=400[/tex] which is true meaning number 1 is a right triangle. [tex]10^{2} +49.5^{2} = 50.5^{2} -- > 100+2450.25=2550.25[/tex] is true meaning number 2 is also a right triangle because the sum of the shortest legs squared are equal to the longest leg (hypotenuse) squared.
4. Use the data below for the calculations.
Average hours sleeping per weeknight: 4, 5, 8, 12, 10, 6, 7, 9, 8, 8, 6, 6, 4, 3, 9
Mean:
Median:
Mean Absolute Deviation:
Absolute Deviation from Median:
The mean is 7
The median is the middle value, which is 7.
Mean Absolute Deviation: 2
How to solve for the mean absolute deviationStep 3: Find the absolute deviation of each value from the mean:
|4-7.067|, |5-7.067|, |8-7.067|, |12-7.067|, |10-7.067|, |6-7.067|, |7-7.067|, |9-7.067|, |8-7.067|, |8-7.067|, |6-7.067|, |6-7.067|, |4-7.067|, |3-7.067|, |9-7.067|
These absolute deviations are: 3.067, 2.067, 0.933, 4.933, 2.933, 1.067, 0.067, 1.933, 0.933, 0.933, 1.067, 1.067, 3.067, 4.067, 1.933.
Step 4: Find the mean of these absolute deviations to find the mean absolute deviation:
Mean Absolute Deviation = (3.067+2.067+0.933+4.933+2.933+1.067+0.067+1.933+0.933+0.933+1.067+1.067+3.067+4.067+1.933) / 15 = 2
Step 5: Find the absolute deviation of each value from the median:
|4-8|, |5-8|, |6-8|, |6-8|, |6-8|, |7-8|, |8-8|, |8-8|, |8-8|, |9-8|, |9-8|, |10-8|, |12-8|, |8-8|, |3-8|
These absolute deviations are: 4, 3, 2, 2, 2, 1, 0, 0, 0, 1, 1, 2, 4, 0, 5.
Therefore, the absolute deviation from the median is 5.
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A) What internal goods does mathematics offer? Discuss how these goods multiply when you share them with others. B) Discuss creative power and coercive power that you have witnessed in mathematical settings. C) How can teachers affirm their students' dignity as creative human beings in the ways they do mathematics?
A) Internal goods in mathematics include problem-solving skills, logical thinking, analytical reasoning, and a deep understanding of mathematical concepts.
B) Coercive power, on the other hand, might manifest when individuals impose their methods or beliefs on others, potentially stifling creativity and discouraging alternative perspectives.
C) Teachers affirm their students' dignity as creative human beings in the ways they do mathematics by creating a safe space, encourage exploration and expression, value the learning process, celebrate creativity and originality in problem-solving
A) When you share these goods with others, they multiply in the sense that others also develop these skills, fostering collaboration, and generating new ideas, ultimately contributing to the overall progress in the field of mathematics.
B) Creative power in mathematical settings can be seen when individuals or teams come up with innovative solutions to problems, develop new theories, or find unique ways to apply mathematics to real-world situations.
C) Teachers can affirm their students' dignity as creative human beings in the ways they do mathematics by:
1. Encouraging students to explore multiple solution methods and strategies, allowing them to find the approach that best suits their thinking style.
2. Valuing each student's input, ideas, and questions, creating a safe and supportive environment for them to express their thoughts.
3. Challenging students with open-ended problems that require creativity and critical thinking, emphasizing the importance of understanding concepts over rote memorization.
4. Recognizing and celebrating each student's unique strengths and contributions to the learning process, promoting a growth mindset and a sense of accomplishment.
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Use a calculator to find the values of the inverse trigonometric functions. Round to the nearest degree.
The values of the inverse trigonometric functions are 72°, 76° and 85°.
How to explain the stepsThe range of the inverse trigonometric function is limited to a certain interval based on the domain of the original trigonometric function.
Its also important to identify the trigonometric ratio that corresponds to the given value.
The value on degree for inverse of sin (2/3) will be 41.81° which is 42°. Also, inverse of tan(4) is 76° using the calculator.
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Use a calculator to find the values of the inverse trigonometric functions. Round to the nearest degree.
inverse of sin (2/3)
inverse of tan(4)
inverse of tan (0.1)
The figure below has semicircles on each side of a 40 meter by 40 meter square. Find the area of the enclosed figure. Round to the nearest tenth
The area enclosed by the circle is given as 7494.12 m² and the mistake Frank have made is he subtracted the area of the square and the area of 4 semi-circles.
We are given that the figure is made by attaching semicircles to each side of a 54 dash m-by-54 dash m square. Frank says the area is 1 comma 662.12 m squared.
We have to find the error made by Frank,
Area of the square = Side of the square x Side of the square
In the question; the side of the square given is 54 m and this would also be the diameter of the semicircle attached to each side of a square.
So, the radius of the semicircle = diameter /2 = 54/2 = 27 m
Now, the area of the square = 54 x 54 = 2916 m².
Also, the area of the semi-circle = [tex]\frac{\pi r^2}{2}[/tex] = [tex]\frac{3.14*27^2}{2}[/tex] = 1144.53 m² .
As there are a total of 4 semi-circles attached to the square, so the area of all the 4 semi-circles = 4 x 1144.53 = 4578.12
Now, the total area of the figure = Area of the square + Area of 4 semi-circles
= 2916 + 4578.12
= 7494.12 m².
The error made by Frank was that he subtracted the area of the square and the area of 4 semi-circles to find the area of the whole figure as (4578.12 - 2916 = 1662.12 ).
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Complete question:
Frank needs to find the area enclosed by the figure. The figure is made by attaching semicircles to each side of a 54 m-by-54 m square. Frank says the area is 1662.12 meter squared. Find the area enclosed by the figure. Use 3.14 for pi. What error might Frank have made?
How to find the area of this whole figure? Please help me
The area of the whole figure is 31.5 sq. units.
What is the area of a figure?The area of a given figure connotes its expanse in a 2 dimensional plane. The shape and size of a given figure determines how to calculate its area.
From the given question, the figure given can be likened to a rhombus. So that;
area of a rhombus = (diagonal 1 * diagonal 2)/ 2
Then,
area of the figure = (diagonal 1 * diagonal 2)/ 2
where: diagonal 1 = 7.5, and diagonal 2 = 8.4
So that;
area of the figure = (7.5*8.4)/ 2
= 63/ 2
= 31.5
The area of the whole figure is 31.5 sq. units.
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Is the triangle similar to PQR? State whether each triangle similar to PQR by answering yes or no
Yes, all three triangles RQS, QSR, and PRS are similar to triangle PQR.
Describe Congruency of triangle?Congruency of triangles refers to the condition in which two or more triangles have the same size and shape. In other words, if two or more triangles have congruent sides and angles, then they are said to be congruent.
The criteria for determining the congruency of triangles are based on the properties of sides and angles. There are various ways to show that two triangles are congruent, including the following:
Side-Side-Side (SSS) Congruence: If the three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.
Side-Angle-Side (SAS) Congruence: If two sides and the angle between them in one triangle are equal to two sides and the angle between them in another triangle, then the two triangles are congruent.
Angle-Side-Angle (ASA) Congruence: If two angles and the side between them in one triangle are equal to two angles and the side between them in another triangle, then the two triangles are congruent.
Angle-Angle-Side (AAS) Congruence: If two angles and a side not between them in one triangle are equal to two angles and the corresponding side not between them in another triangle, then the two triangles are congruent.
Hypotenuse-Leg (HL) Congruence: If the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.
Yes, all three triangles RQS, QSR, and PRS are similar to triangle PQR.
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The probability that Sam parks in a no-parking zone and gets a parking ticket is 0. 07,and the probability that Sam Connor finr a legal parking space and has to park in the no-parking zone is 0. 50. On Monday,Sam arrives at school and has to park in a no-parking zone. Find the probability that he will get a parking ticket.
The probability that Sam will get a parking ticket given that he has to park in a no-parking zone on Monday is approximately 0.1308 or 13.08%.
We can use Bayes' theorem to solve this problem. Let A be the event that Sam gets a parking ticket and B be the event that Sam parks in a no-parking zone. Then, we want to find P(A|B), which is the conditional probability of A given B.
Bayes' theorem states that P(A|B) = P(B|A)*P(A)/P(B), where P(B|A) is the probability of B given A, P(A) is the prior probability of A, and P(B) is the prior probability of B.
From the problem, we know that P(A) = 0.07, P(B|A) = 1 (since if Sam parks in a no-parking zone, he will definitely get a parking ticket), and P(B|not A) = 0.50 (since if Sam finds a legal parking space, he has a 0.50 probability of parking in a no-parking zone).
To find P(B), we can use the law of total probability, which states that P(B) = P(B|A)*P(A) + P(B|not A)*P(not A), where P(not A) = 1 - P(A).
Therefore, P(B) = 10.07 + 0.50(1-0.07) = 0.5351.
Finally, we can use Bayes' theorem to find P(A|B):
P(A|B) = P(B|A)P(A)/P(B) = 10.07/0.5351 ≈ 0.1308.
Therefore, the probability that Sam will get a parking ticket given that he has to park in a no-parking zone on Monday is approximately 0.1308 or 13.08%.
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I NEED HELP PLEASE!
1. 3 statements about limiting frictional force between two surfaces are given below.
A - Nature of surfaces in contact affects to limiting frictional force.
B - Normal reaction between them affects to limiting frictional force.
C - Area of surfaces in contact affects to limiting frictional force.
Correct statement / statements from above A, B, C is/ are,
(1) A
(2) B
(3) A and C
(4) A, B and C
The limiting frictional force depends only on:
A. The nature of surfaces in contact: Rough and irregular surfaces have higher friction than smooth surfaces. C. The area of surfaces in contact: Larger the contact area, higher is the friction between the surfaces.(3) A and C is the right optionA pyramid has a base that is a regular hexagon with each side measuring 10 units. The base of the pyramid is shown below.If the pyramid has a height of 12 units, what is the approximate volume of the pyramid?
Answer:
Step-by-step explanation:
The volume of a pyramid can be calculated using the formula:
V = (1/3) * Base Area * Height
To calculate the volume of this pyramid, we need to first find the area of its regular hexagonal base. The formula for the area of a regular hexagon is:
A = (3√3/2) * s^2
where s is the length of one side of the hexagon. Substituting s = 10, we get:
A = (3√3/2) * 10^2 = 259.80 square units (approx)
Now we can use the formula for the volume of a pyramid to find the volume of this pyramid:
V = (1/3) * 259.80 * 12 = 1039.20 cubic units (approx)
Therefore, the approximate volume of the pyramid is 1039.20 cubic units.
A three digit number is such that twice the hundreds digit is more than the tens digit by 2. The unit digit is thrice the hundred digit. When the digits are reversed the number is increased by 594. Find the number.(5 marks)
Answer:
Step-by-step explanation:
Let the three-digit number be represented as $abc$, where $a$ is the hundreds digit, $b$ is the tens digit, and $c$ is the units digit.
From the problem, we have two equations:
Equation 1: $2a=b+2$
Equation 2: $c=3a$
We can use these equations to solve for $a$, $b$, and $c$.
Starting with Equation 1, we can isolate $b$ to get $b=2a-2$.
Next, we can substitute Equation 2 into Equation 1 to get $2a=3a-6+2$, which simplifies to $a=8$.
Using this value of $a$, we can now find $b$ and $c$. From Equation 2, we have $c=3a=24$. And from Equation 1, we have $b=2a-2=14$.
Thus, the original three-digit number is $abc=824$.
When we reverse the digits to get $cba=428$, we increase the number by 594, so we have $cba=abc+594=824+594=1418$.
Therefore, the answer is $\boxed{824}$.
Find the area of the polygon.
18 m
29 m
36 m
The area of the polygon is 14
14 m
square meters.
The total area of the composite figure is 576 square meters
Calculating the area of the polygon figureFrom the question, we have the following parameters that can be used in our computation:
The composite figure
The total area of the composite figure is the sum of the individual shapes
So, we have
Surface area = Rectangle + Trapezoid
Using the area formulas, we have
Surface area = 29 * 16 + 1/2 *(14 + 18) * (36 - 29)
Evaluate
Surface area = 576
Hence. the total area of the figure is 576 square meters
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Complete question
Find the area of the polygon.
See attachment
The area of the polygon is ____ square meters.
In the formula
A(t) = Pert for continuously compound interest, the letters P, r, and t stand for ---Select--- percent interest prime rate amount after t years principal number of years , ---Select--- interest rate per year rate of return investment amount investment per year interest rate per day , and ---Select--- number of months number of days number of time periods number of years number of times interest is compounded per year , respectively, and A(t) stands for ---Select--- amount of principal amount after t days amount of interest earned after t years amount of interest earned in year t amount after t years. So if $200 is invested at an interest rate of 4% compounded continuously, then the amount after 3 years is $. (Round your answer to the nearest cent. )
In the formula [tex]A(t) = Pe^{rt}[/tex] continuously compound interest P, r, and t stands for Principal, rate of interest, and time respectively, and A(t) stands for Amount after t amount of time. If $200 is invested at an interest rate of 4% compounded continuously, then the amount after 3 years is $225.5.
The formula for Compound Interest at a continuous period of time is denoted by [tex]A(t) = Pe^{rt}[/tex]
where the Principal amount is multiplied by the exponential value of the interest rate and time passed.
Hence we are given here
P = $200, r = 4% = 0.04, and the amount to be calculated for t = 3 years
Hence we will find the amount by replacing these values to get
A(3) = 200 × e⁰°⁰⁴ ˣ ³
= $200 × e⁰°¹²
= $225.499
rounding it off to the nearest cent gives us
$225.5
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Correct Question
In the formula [tex]A(t) = Pe^{rt}[/tex] continuously compound interest P, r, and t stands for ______ , _______ , and __________ respectively, and A(t) stands for _______ .
So if $200 is invested at an interest rate of 4% compounded continuously, then the amount after 3 years is $__________. (Round your answer to the nearest cent.)
Here is a set of data showing the test scores for US History class:
56, 88, 70, 72, 90, 85, 99, 65, 66, 54, 74, 85, 91, 92, 72, 88, 97, 62, 88 Create a stem and leaf plot to show this data. Hint: Decide how many stems you will need.
can somebody help me ?
Hi! I'd be happy to help you create a stem and leaf plot using the provided set of data for US History class test scores.
Step 1: Arrange the data in ascending order.
54, 56, 62, 65, 66, 70, 72, 72, 74, 85, 85, 88, 88, 88, 90, 91, 92, 97, 99
Step 2: Determine the range of the data.
The data ranges from 50s to 90s, so we will need 5 stems: 5, 6, 7, 8, and 9.
Step 3: Create the stem and leaf plot using the stems and corresponding leaves (the units digits of the data).
5 | 4 6
6 | 2 5 6
7 | 0 2 2 4
8 | 5 5 8 8 8
9 | 0 1 2 7 9
Here is the completed stem and leaf plot for the US History class test scores. The stems represent the tens digits (50s, 60s, 70s, 80s, 90s), and the leaves represent the units digits of the scores in each range.
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Solve problems 1 and 4 ONLY with the rules given on the paper.
The solution to the equations obtained using inverse trigonometric function values are;
1. x ≈ 0.65
4. x ≈ 0.95
What are trigonometric functions?Trigonometric functions indicates the relationships between the angles in a right triangle and two of the sides of the triangle. Trigonometric functions are periodic functions.
The value of x is obtained from the inverse trigonometric function of the output value of the trigonometric function, as follows;
The inverse function for sine is arcsine
The inverse function for cosine is arccosine
The inverse function for the tangent of an angle is arctangent
1. sin(x) = 0.6051
Therefore; x = arcsine(0.6051) ≈ 0.65 radians
The value of x in the interval [0·π, 2·π] is x ≈ 0.65
4. tan(x) = 1.3972
Therefore, x = arctan(1.3972) ≈ 0.95
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The cone is formed from 3,200 ft3 of gravel. If the height of the cone is 24 feet, what is the radius, in feet, of the base of the cone? Use the π button on your calculator to determine the answer. Round your answer to the nearest tenth of afoot. The radius of the base of the cone is approximately ____ feet
The radius of the base of the cone is approximately 12.65 feet if The cone is formed from 3,200 ft of gravel.
Height of cone = 24 feet
The volume of the cone = [tex]3,200 ft^3[/tex]
To find the volume of the cone, the formula used here is:
V =π* [tex]r^2h[/tex]
Here, the values of V and H are known terms. we need to calculate the radius r of the cone.
π = 3.14 constant value
Substituting the values in the above equation, we get:
[tex]3,200 = (1/3)^2*(24)*[/tex] π
[tex]r^2[/tex]= 3,200 / (8π)
[tex]r^2[/tex] = 400 / π
r = 12.65
Therefore, we can conclude that the radius of the base of the cone is 12.65 feet.
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A string has a length of 80 cm. It is cut into pieces in the ratio 1: 4: 5. Calculate the length of the longest piece.
First, we need to find the total number of parts in the ratio 1:4:5:
1 + 4 + 5 = 10
This means that the string is divided into 10 equal parts. To find the length of each part, we divide the total length of the string by the number of parts:
80 cm ÷ 10 = 8 cm
Now, we can find the length of the longest piece, which is 5 times the size of each part:
8 cm x 5 = 40 cm
Therefore, the length of the longest piece is 40 cm.
