Answer:
First, we need to figure out how many circular rugs can fit in the living room without overlap.
One way to approach this is to find the area of each circular rug (using the formula A = πr^2, where r = 3 feet since the diameter is 6 feet).
A = π(3)^2 = 28.26 square feet
Next, we can find the area of the living room:
A = 12 x 18 = 216 square feet
To figure out how many circular rugs can fit, we can divide the living room area by the rug area:
216/28.26 ≈ 7.64
Since we can't have partial rugs, we need to round down, which means Shannon can fit 7 circular rugs in her living room without overlap.
The total area covered by the circular rugs would be:
7 x 28.26 = 197.82 square feet
Therefore, the closest answer choice to the nearest square foot is A) 170 ft².
Answer:A
Step-by-step explanation:
She can put 2 circles together width wise because 6+6 = 12
She can put 3 circles together length wise because 6+6+6 = 18
So she can put 6 circles in total.
The area of one circle is found with the equation A=πr^2
The diameter is 6ft, so the radius is 3ft, so
A=π*3ft^2
A=28.26ft²
This is the area of one circle. We need to find the area of 6 because 6 can fit in total.
28.26ft² * 6= 169.56 ft²
Calling card A charges a connect fee of 69¢ plus 1.9¢ perminute. Calling card B has no connect fee but charges 6¢ perminute.
Which system of equations can be used to determine the number of minutes (x) where the price (y) is the same for both cards?
Answer:
16.829 minutes
Step-by-step explanation:
To solve this problem, we need to set up a system of equations based on the given information. Let's define the variables:
Let x be the number of minutes.
Let y be the price in cents.
For calling card A, the price can be calculated using the formula: y = 69 + 1.9x
For calling card B, the price can be calculated using the formula: y = 6x
We want to find the number of minutes (x) where the price (y) is the same for both cards. To set up the system of equations, we equate the two expressions for y:
69 + 1.9x = 6x
Now, we can solve this equation to find the value of x, which represents the number of minutes where the prices are equal.
69 + 1.9x = 6x
To simplify the equation, we can subtract 1.9x from both sides:
69 = 6x - 1.9x
Combining like terms, we have:
69 = 4.1x
To isolate x, we divide both sides of the equation by 4.1:
69 / 4.1 = x
Simplifying the division gives us:
16.829 = x
Therefore, the number of minutes (x) where the price (y) is the same for both calling cards A and B is approximately 16.829 minutes.
Hope this helps!
Answer:
For calling card A: y = 0.019x + 0.69
For calling card B: y = 0.06x
Step-by-step explanation:
For calling card A: y = 0.019x + 0.69
For calling card B: y = 0.06x
Set the prices equal to each other to find when they are the same:
0.019x + 0.69 = 0.06x
Simplify and solve for x:
0.041x = 0.69
x = 16.83 (rounded to two decimal places)
Therefore, if a person expects to talk for 16.83 minutes or more, calling card A will be cheaper. If they expect to talk for less than 16.83 minutes, calling card B will be cheaper.
What value of x would make 5 Superscript x Baseline equals 625 true? Enter the answer in the box
The value of x that makes [tex]5^x = 625[/tex] true is x = 4.
To determine the value of x in the equation [tex]5^x = 625[/tex], we need to find the exponent that results in 625 when applied to the base 5.
Since 625 can be expressed as 5 raised to the power of 4 ([tex]5^4 = 625[/tex]), the value of x that satisfies the equation is 4.
When we substitute x = 4 into the equation, we get [tex]5^4 = 625[/tex], which is true.
Therefore, x = 4 is the solution to the equation, indicating that 5 raised to the power of 4 equals 625.
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287 megabytes downloaded if 14.4% complete how many are downloaded? Round to nearest tenth
Answer:
To find out how many megabytes have been downloaded, we can multiply 287 by 0.144 (which represents 14.4% as a decimal).
The calculation is:
287 x 0.144 = 41.328
Rounded to the nearest tenth, the number of megabytes downloaded is 41.3.
which of the following angle pairs represent consultative interior angles please help
The correct option is b, the pair of consecutive interior angles is 1 and 7.
Which of the following angle pairs represent consultative interior angles?
First, we can see that the interior angles are the angles that are "interior" to the intersections.
These are 1, 4, 6, and 7.
Because the two lines are parallel, the consecutive interior angles are angles that would be adjacent (add up to 180°) but that are in different intersections.
Then the consecutive interior angles are:
3 and 6
1 and 7
The correct option is b.
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a rocket is launched in the air. Its height in feet is given by h=-16t^2+128t where t represents the time in seconds after launch. What is the appropriate domain for this solution?
The quadratic function has the following domain: 0 ≤ t ≤ 8.
How to find the domain of a quadratic equation
Herein we find a quadratic equation that models the height of the rocket in time. The domain is the set of all values of t such that all values of h exist.
Mathematically speaking, the domain of quadratic equations is the set of all real numbers, but physically speaking, this domain is formed by the set of all non-negative numbers such that h ≥ 0. The domain is found by algebra properties:
h = - 16 · t² + 128 · t
h = - 16 · t · (t - 8)
Then, the domain of the quadratic function is: 0 ≤ t ≤ 8.
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PLS HELP WILL GIVE BRAINLIEST IF CORRECT (NO LINKS)
Find the measure of arc BC.
Answer: A 129
Step-by-step explanation:
Because the 2 chords are the same (lines in the circle), the 2 arcs are the same create an equation that makes them equal
3x+24 = 4x -11 >bring x to one side by subtracting both sides by 3x
24 = x -11 > add both sides by 11
35 = x
Now that we have solved for x you need to plug that back into the equation for BC
BC= 4x-11
BC = 4(35) - 11
BC = 140 - 11
BC = 129 >A
Test a claim on three locations ?
The slope constraint for the zip line is 6 to 8 feet of vertical change for every 100 feet of horizontal change.
How to explain the informationSo, if the vertical change is 7 feet, the horizontal change must be between 7/6 and 7/8 of a hundred feet, or between 11.67 and 12.5 feet.
For Zip line A, the horizontal distance is 120 feet. So, the vertical change of 7 feet is within the slope constraint.
For Zip line B, the horizontal distance is 140 feet. So, the vertical change of 7 feet is within the slope constraint.
For Zip line C, the horizontal distance is 150 feet. So, the vertical change of 7 feet is within the slope constraint.
Therefore, LaTisha's claim is correct. The vertical change of 7 feet will satisfy the slope constraint for all three locations.
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A circle is inscribed inside a square of a side length of 10 cm. What is the area inside the square and outside the circle
Answer:
The figure is omitted--please sketch it to confirm my answer.
[tex]\pi {(5 \sqrt{2}) }^{2} - {10}^{2} [/tex]
[tex]50\pi - 100 = 50(\pi - 2) = 57.08[/tex]
The area inside the square and outside the circle is about 57.08 cm^2.
33 + 78 + 10 + 98 + 76
Answer:
The sum of 33, 78, 10, 98, and 76 is 295.
Answer:
295
Step-by-step explanation:
add the numbers by using the addiction sign
find the surface area
400Answer:
Step-by-step explanation:
Will someone please answer this and show me how you got it
(a) Using Excel, the calculations are shown below:
Mean = 608.67
Median = 610.00
Mode = 610.00
Standard Deviation = 96.89
(b) The measure of central tendency would be appropriate are the median and the mode.
How do we calculate?The median is fitting because it is a representation of the middle value in the data set and is not affected by extreme values.
We can see that our median rent is $610.00 and an appropriate representation of the typical rent paid by the students.
The mode is $610.00 and also an indication that this rent amount is the most common among the students.
In conclusion, a measure of the variability or dispersion in the data set is provided by the standard deviation, which is determined to be 96.89. It demonstrates how widely the rents vary from the mean.
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer: D = 100π square units
Step-by-step explanation:
The formula to calculate the circumference of a circle is C = 2πr, where C is the circumference and r is the radius of the circle.
In this case, we have a circumference of 20π units, so we can set up the equation as follows:
20π = 2πr
To find the radius, we can divide both sides of the equation by 2π:
r = (20π) / (2π)
Simplifying further:
r = 10
Now that we have the radius, we can calculate the area of the circle using the formula A = πr^2:
A = π * (10)^2
A = π * 100
A = 100π
Find the derivative of f(w) = 2/(w^2-4)^5
The derivative of function f(w) = [tex]2/(w^2 - 4)^5 ~is ~f'(w) = -40~w~(w^2 - 4)^{-6}.[/tex]
We have,
To find the derivative of the function [tex]f(w) = 2/(w^2 - 4)^5[/tex], we can use the chain rule and the power rule for differentiation.
Let's go through the steps:
First, rewrite the function as [tex]f(w) = 2(w^2 - 4)^{-5}.[/tex]
Now, let's differentiate f(w) with respect to w:
[tex]f'(w) = d/dw~ [2(w^2 - 4)^{-5}][/tex]
To apply the chain rule, we need to differentiate the outer function and multiply it by the derivative of the inner function.
Using the power rule, the derivative of (w² - 4) with respect to w is 2w.
Applying the chain rule:
[tex]f'(w) = -10 \times 2(w^2 - 4)^{-6} \times 2w[/tex]
Simplifying further:
[tex]f'(w) = -40w(w^2 - 4)^{-6}[/tex]
Therefore,
The derivative of function f(w) = [tex]2/(w^2 - 4)^5 ~is ~f'(w) = -40~w~(w^2 - 4)^{-6}.[/tex]
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What is the sum of the exterior angles in a regular 20-gon?
The sum of the exterior angles in a regular 20-gon is given as follows:
360º.
How to obtain the sum of the exterior angles?An exterior angle of a polygon is defined as the angle between a side and its adjacent extended side.
The sum of exterior angles formula states the sum of all exterior angles in any polygon is 360°, no matter the number of sides.
For this problem, we have a 20-gon, that is a polygon of 20 sides, however, as the formula states, the sum of the exterior angles in a regular 20-gon is given as follows:
360º.
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thomas has a cube with the numbers 3,4,5,7,8 and 9 written on its faces. he rolls the cube twice and records the outcome. What is the probability that both numbers are greater than 5.
a) 1/9 b)1/4 c)1/5 d)1/16
Answer:
None of the options provided (a, b, c, d) matches the correct probability. The correct probability is 1/18.
Step-by-step explanation:
After drawing a square on the board, Mr. Hinkle asked his class to identify the shape. Timothy stated that Mr. Hinkle had drawn a rhombus. Which of the following statements is true?
What is the equation of a circle, if the end points of its
longest chord are (4, -3) and (-2,5)?
Answer:
The answer is D, the last one.
A dinner theater has fixed costs of $1,000 per day. It costs the dinner theater $10 per person for food and a
ticket to the dinner theater costs $30. How many tickets does the dinner theater have to sell in order to break
even?
50 tickets
O 10 tickets
O 100 tickets
O20 tickets
(09.03 MC)
The daily temperature in the month of February in a certain country varies from a low of 28°F to a high of 50°F. The temperature reaches the
freezing point of 32°F when time (t) is 0 and completes a full cycle in 8 hours. What is the amplitude, period, and midline of a function that
would model this periodic phenomenon?
O a
Ob
Oc
Od
Amplitude 11°F; period - 8 hours; midline: y = 39
Amplitude 11°F; period=4 hours; midline: y = 11
Amplitude = 22°F; period - 8 hours; midline: y = 39
Amplitude = 22°F; period - 4 hours; midline: y = 11
Answer:
The correct answer is:
Amplitude = 11°F; period = 8 hours; midline: y = 39
Step-by-step explanation:
Answer: A
Step-by-step explanation: Amplitude 11°F; period - 8 hours; midline: y = 39
Anna wants to determine the height of a right rectangular prism. The prism has a volume of 380 cm³ and a base whose area is 50 cm². She lets h represent the height of the prism.
What equation can she write to solve the problem?
The height of the right rectangular prism is 7.6 cm.
To determine the height of the right rectangular prism, we can use the formula for the volume of a prism:
Volume = Base Area * Height
Given that the volume is 380 cm³ and the base area is 50 cm², we can write the equation as:
380 = 50 * h
Now, let's solve for h by dividing both sides of the equation by 50:
h = 380 / 50
Simplifying the expression:
h = 7.6 cm
Therefore, the height of the right rectangular prism is 7.6 cm.
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Solve for x and graph the solution on the number line below.
V
V
VI
11 2x-5 or 2x-5 > 15
IV.
Inequality Notation:
Number Line:
or
-12 -10 -8 -6
-4
-2
O
2
4
6
8
10 12
x ≤ 8 or x > 10 is the solution of the inequality 11 ≥ 2x - 5 or 2x - 5 > 15.
To solve the compound inequality 11 ≥ 2x - 5 or 2x - 5 > 15, we will solve each inequality separately and then combine the solutions.
Solve the first inequality: 11 ≥ 2x - 5
Add 5 to both sides to isolate 2x:
11 + 5 ≥ 2x
16 ≥ 2x
Divide both sides by 2:
8 ≥ x
So the solution to the first inequality is x ≤ 8.
Solve the second inequality: 2x - 5 > 15
Add 5 to both sides to isolate 2x:
2x > 15 + 5
2x > 20
Divide both sides by 2:
x > 10
So the solution to the second inequality is x > 10.
Combining the solutions, we have x ≤ 8 or x > 10.
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Which statement is true? 3x-4y=4 or 3x-4y=8
Answer:3x-4y=8
Step-by-step explanation:
Find the value of x in the equation, 3^2x-1 = 81
Step-by-step explanation:
3^(2x-1) = 81 LOG both sides I had to assume there were parens.
(2x-1) LOG 3 = LOG 81
2x-1 = LOG(81) / (LOG 3) = 4
2x = 5
x = 2.5
stuck on this question any help would be appreciated :)
The points that represent this data set are shown in the scatter plot attached below.
How to construct and plot the data in a scatter plot?In this exercise, we would plot the number sold on the x-coordinates of a scatter plot while the prices ($) would be plotted on the y-coordinate of the scatter plot through the use of Microsoft Excel.
On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display a linear equation for the line of best fit on the scatter plot.
Based on the scatter plot shown below, which models the relationship between the number sold and the prices ($), a linear equation for the line of best fit is as follows:
y = 0.23x + 1.00
In conclusion, the slope of the line is 0.23 and the y-intercept is 1.00.
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round 52754.1683 the nearest.ten
Answer:
52750
Step-by-step explanation:
Step 1: Identify the digit in the tens place:
The digit in the tens place is always 2 spaces to the left of the decimal.Thus, the digit in the tens place is 5 (the one sandwiched between 7 and 4).Step 2: Examine the digit to the right of the tens place:
In this case, the digit to the right of the tens place is 4.Step 3: Determine the rounding:
When the digit to the right of the tens place is 5 or greater (5, 6, 7, 8, or 9), you round up the tens place digit by adding 1 to the digit in the tens place.Also, we remove the decimal point and everything to the left of it, using a whole number only.When the digit to the right of the tens place is less than 5 (4, 3, 2, 1, or 0), you keep the tens place digit as it is and the number to right of tens place digit it replaced by 0.We still remove the decimal point and everything to the left of it, using a whole number only.Since the digit to the right of the tens place is 4 (which is less than 5), we keep the tens place digit as is.
Original number: 52754.1683
Rounding to the nearest ten: 52750
Thus, rounding 52754.1683 to the nearest ten gives us 52750.
1. What are two significant advantages of a 401(k) over an IRA?
Here are two significant advantages of a 401(k) over an IRA:
Higher Contribution LimitsEmployer Contributions and MatchingThe two significant advantages of a 401(k) over an IRAHigher Contribution Limits: 401(k) plans allow for higher annual contributions compared to IRAs. The contribution limit for a 401(k) is $19,500 (or $26,000 for individuals aged 50 and older), while the limit for an IRA is $6,000 (or $7,000 for individuals aged 50 and older).
Employer Contributions and Matching: 401(k) plans often offer employer contributions and matching programs. Employers may contribute to an employee's 401(k) account, adding to their retirement savings without any direct cost to the employee.
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What is the lateral surface area of the triangular prism below?
The lateral surface area of the triangular base prism is 288 m².
How to find the lateral area of a triangular prism?The lateral area of the triangular base prism can be found as follows:
Lateral area of the triangular base prism = (a + b + c)h
where
a, b and c are the side of the triangleh = height of the prismTherefore,
a = 7 m
b = 8 m
c = 9 m
h = 12 m
Therefore,
Lateral area of the triangular base prism = (7 + 8 + 9)12
Lateral area of the triangular base prism = 24 × 12
Lateral area of the triangular base prism = 288 m²
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The graph shows the number of weeks of practice (x) and the number of
shots missed in a free-throw drill (y). The equation of the trend line that best
fits the data is y = - + 6. Predict the number of missed shots after 10
weeks of practice.
A. 1
B. 2
C. 3
D. 4
The number of missed shots after 10 weeks of practice is 1
Predicting the number of missed shots after 10 weeks of practice.From the question, we have the following parameters that can be used in our computation:
The line of best fit
Also, we have the equation to be
y = -1/2x + 6
At the 10th weeks, we have
x = 10
Substitute the known values in the above equation, so, we have the following representation
y = -1/2 * 10 + 6
Evaluate
y = 1
Hence, the number of missed shots after 10 weeks of practice is 1
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For what value of x is the rational expression below equal to zero?
x-9
(x-4)(x+4)
OA. -4
B.
C.-9
D. 9
SUBMIT
The value of x is 9
To find the value of x for which the rational expression is equal to zero, we need to set the numerator equal to zero:
x - 9 = 0
Solving for x:
x = 9
Therefore, the value of x = 9.
Looking at the denominator (x - 4)(x + 4), we see that it contains two factors: (x - 4) and (x + 4). For the entire expression to equal zero, either the numerator or one of the factors in the denominator must equal zero.
Setting each factor in the denominator equal to zero:
x - 4 = 0 or x + 4 = 0
x = 4 or x = -4
These are the valid values of x for which the rational expression is equal to zero.
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What is the area of the rectangle above?
OA. 96 square units
OB. 20 square units
OC. 104 square units
OD. 40 square units
The area of the rectangle with a length of 12 units and a width of 8 units is 96 sqaure units.
How to determine the area of a rectangle?A rectangle is a 2-dimensional shape with parallel opposite sides equal to each other and four angles are right angles.
The area of a rectangle is expressed as;
Area = length × breadth
From the image:
Length of the rectangle = 12 units
Breadth of the rectangle = 8 units
Area of the rectangle = ?
Plug the given values into the above formula and solve for the area:
Area = length × breadth
Area = 12 units × 8 units
Area = 96 sqaure units
Therefore, the measure of the area is 96 sqaure units.
Option A) 96 sqaure units is the correct answer.
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