(a) Miguel had the greatest spread in training times.
(b) The middle 50% of Adam's training times had the least spread.
(a) To find the greatest spread in training times, we need to calculate the range of each person's training times. Range is the difference between the maximum and minimum values. Comparing the ranges, we can say that Miguel had the greatest spread in training times since his range is the largest.
(b) The middle 50% of the training times refers to the interquartile range (IQR), which is the difference between the third quartile (Q3) and the first quartile (Q1).
To find the least spread in the middle 50% of the training times, we need to compare the IQRs of each person. Adam's IQR is the smallest, which means the middle 50% of his training times had the least spread.
(c) The answers to parts (a) and (b) indicate that Miguel had a wider range of training times compared to Adam. However, Adam's middle 50% of training times had the least spread. This suggests that while Miguel's overall training times varied more, Adam's training times were more consistent within the middle range.
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cos 14° -sin 14°/ cos 14° + sin 14° = cot 59
Answer:
To solve this trigonometric identity, we need to use the definitions of the trigonometric functions and some algebraic manipulation. Here's how we can do it:
cos 14° - sin 14°/ cos 14° + sin 14°
= (cos 14°/cos 14°) - (sin 14°/cos 14°)/(cos 14°/cos 14°) + (sin 14°/cos 14°) (multiplying the numerator and denominator of the second term by cos 14°)
= 1 - tan 14°/1 + tan 14° (using the definitions of cosine and sine, and dividing both terms by cos 14°)
= (1 - tan²14°)/(1 + tan 14°) (using the identity 1 + tan²θ = sec²θ)
= 1/cot 14° - cot 14° (using the definition of cotangent and simplifying the numerator)
= cot 90° - cot 14° (using the identity cot(90° - θ) = tan θ)
= cot (90° + 14°) (using the identity cot(θ + 90°) = -tan θ)
= cot 104°
Since cot(104°) = cot(180° - 76°) = -cot 76°, we can also write the final answer as -cot 76°.
Therefore, the given identity is true, and we have shown that:
cos 14° - sin 14°/ cos 14° + sin 14° = cot 59 = -cot 76°.
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The equation The equation y=5,520x -1,091 was given for the line of best fit. What does the slope of the line mean in the context of this problem? was given for the line of best fit. What does the slope of the line mean in the context of this problem?
The slope of the line is 5,520 and it means the price of the diamond increases at a rate of 5,520 per diamond's weight.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + c
Where:
m represents the slope or rate of change.x and y are the points.c represents the y-intercept or initial value.Based on the information provided about this situation, it can be modeled by this linear equation:
y = mx + c
y = 5,520x - 1,091
By comparison, we have the following:
Slope, m = 5,520.
y-intercept, c = -1,091.
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Complete Question:
The function described by the equation y =5,520x - 1,091 is a model of the relationship between a diamond's weight and its price. What does the slope of the line mean in the context of this problem?
Dolly went to the Walmart and he buy 14 teddy bears and 3 dolls for 158 $ and her sister went to the Gwinnett place mall and she buy 8 teddy bears and 12 dolls for 296 $. If they both buy same brand bears and dolls, then what is price of one teddy bear and one doll? (use matrices multiplication to solve system of equations. ) (Show work)
According to formed equations, the price of one teddy bear and one doll is $7 and $20 respectively.
Let us represent the teddy bear as x and dolls as y. Now, framing the equation for Dolly and Gwinnett.
Cost of teddy bear × number + cost of dolls × number = total expenditure
14x + 3y = 158 : equation 1
8x + 12y = 296 : equation 2
Divide the equation by 4
2x + 3y = 74 : equation 3
Subtraction equation 3 from equation 1
14x + 3y = 158
- 2x + 3y = 74
12x = 84
x = 84/12
x = $7
So, the cost of teddy bear = $7
keep the value of x in equation 3 to find the cost of y
2×7 + 3y = 74
14 + 3y = 74
3y = 74 - 14
3y = 60
y = 60/3
y = $20
Thus, the cost of teddy bear and dolls are $7 and $20.
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7. For the function f(x) = -5.5 sin x + 5.5 cos x on a. Find the intervals for which f is concave up and concave down on [0,2π]. CCUP_________ CC DOWN______
b. Identify the coordinates of any points of inflection for fon [0,2π].
a. For the function, the interval for which f is concave down on [0,2π] is (π/4, 5π/4).
CCUP: (0, π/4) and (5π/4, 2π)
CCDOWN: (π/4, 5π/4)
b. The coordinates of the points of inflection are (π/4, 2.45) and (5π/4, -5.95).
a. To find the intervals for which f is concave up and concave down on [0,2π], we need to determine the second derivative of the function f(x):
f(x) = -5.5 sin x + 5.5 cos x
f'(x) = -5.5 cos x - 5.5 sin x
f''(x) = 5.5 sin x - 5.5 cos x
To find where f is concave up (CCUP), we need to find where f''(x) > 0. Thus, we solve the inequality:
5.5 sin x - 5.5 cos x > 0
sin x > cos x
This inequality holds for 0 < x < π/4 and 5π/4 < x < 2π. Therefore, the intervals for which f is concave up on [0,2π] are (0, π/4) and (5π/4, 2π).
To find where f is concave down (CCDOWN), we need to find where f''(x) < 0. Thus, we solve the inequality:
5.5 sin x - 5.5 cos x < 0
sin x < cos x
This inequality holds for π/4 < x < 5π/4. Therefore, the interval for which f is concave down on [0,2π] is (π/4, 5π/4).
Thus, we have:
CCUP: (0, π/4) and (5π/4, 2π)
CCDOWN: (π/4, 5π/4)
b. To find the coordinates of any points of inflection for f on [0,2π], we need to find where the concavity changes, i.e., where f''(x) = 0 or is undefined. Thus, we solve the equation:
5.5 sin x - 5.5 cos x = 0
sin x = cos x
This equation holds for x = π/4 and x = 5π/4.
To determine the concavity at these points, we can examine the sign of f''(x) in the intervals surrounding these points:
For x in (0, π/4), f''(x) < 0, so f is concave down.
For x in (π/4, 5π/4), f''(x) > 0, so f is concave up.
For x in (5π/4, 2π), f''(x) < 0, so f is concave down.
Therefore, the points of inflection for f on [0,2π] are (π/4, f(π/4)) and (5π/4, f(5π/4)).
To find the coordinates of these points, we can substitute π/4 and 5π/4 into the original function:
f(π/4) = -5.5 sin(π/4) + 5.5 cos(π/4) = -2.75 + 5.5/√2 ≈ 2.45
f(5π/4) = -5.5 sin(5π/4) + 5.5 cos(5π/4) = -2.75 - 5.5/√2 ≈ -5.95
Therefore, the coordinates of the points of inflection are (π/4, 2.45) and (5π/4, -5.95).
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Question 10(Multiple Choice Worth 2 points)
(Comparing Data MC)
The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 9.5 to 24 on the number line. A line in the box is at 15.5. The lines outside the box end at 2 and 30. The graph is titled Burger Quick.
Which drive-thru typically has more wait time, and why?
Burger Quick, because it has a larger median
Burger Quick, because it has a larger mean
Super Fast Food, because it has a larger median
Super Fast Food, because it has a larger mean
Question 11(Multiple Choice Worth 2 points)
(Creating Graphical Representations MC)
The number of carbohydrates from 10 different tortilla sandwich wraps sold in a grocery store was collected.
Which graphical representation would be most appropriate for the data, and why?
Circle chart, because the data is categorical
Line plot, because there is a large set of data
Histogram, because you can see each individual data point
Stem-and-leaf plot, because you can see each individual data point
Question 12(Multiple Choice Worth 2 points)
The answer to the first question is: Burger Quick, because it has a larger median.
The answer to the second question is: Histogram, because it can show the frequency distribution of the continuous variable "number of carbohydrates" and group the data into intervals.
What is a histogram?A histogram is a graphical representation of a distribution of numerical data. It consists of a series of bars, where each bar represents a range of values of the data and the height of the bar indicates the frequency or count of data points falling within that range.
In a histogram, the horizontal axis represents the range of values or intervals of the data, called bins, and the vertical axis represents the frequency or count of data points falling within each bin. The bins can be of equal or unequal width depending on the nature of the data.
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Mike calculated the net sales for his company using the following figures:
Gross sales = $50,000
Discounts = $1,800
Freight in = $2,750
Sales returns and allowances = $4,380
The net sales of the company are __________.
a. )
$46,570
b. )
$49,830
c. )
$43,820
d. )
$41,070
To calculate the net sales, we need to subtract the discounts, sales returns and allowances, and freight in from the gross sales.
Therefore, we have:
Net sales = Gross sales - Discounts - Sales returns and allowances - Freight in
Substituting the given values, we get:
Net sales = $50,000 - $1,800 - $4,380 - $2,750 = $41,070
Therefore, the net sales of the company are $41,070. Answer: (d).
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During one week, Sheila made several changes to her bank account. She made four withdrawals of 40$ each from an ATM she also used her check card for a 156$ purchase then she deposited her paycheck of $375
The amount change in her bank account during that week after withdrawals and deposit is equal to $59.
Total number of withdrawals made by Sheila = 4
Amount made at the time withdrawals using ATM = $40
Amount withdraw using check card to purchase = $156
Amount deposited using paycheck = #375
Let us calculate the total amount of money Sheila withdrew from her bank account using ATM,
4 withdrawals of $40 each
= 4 x $40
= $160
So, she withdrew $160 and made a $156 purchase, meaning she spent a total amount of,
= $160 + $156
= $316
Sheila also deposited her paycheck of $375, so the total amount of money in her account changed by is equal to,
$375 - $316 = $59
Therefore, the amount in Sheila's account increased by $59 during that week.
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The above question is incomplete, the complete question is:
During one week, Sheila made several changes to her bank account. She made four withdrawals of $40 each from an ATM. She also used her check card for a $156 purchase. Then she deposited her paycheck of $375. By how much did the amount in her bank account change during that week?
Please help me on this!
The correct point which is solution of equation of line is,
⇒ (1, 2)
We have to given that;
Equation of line is,
⇒ 3x - y = 1
Take a point 2,
⇒ (1, 2) = (x, y)
Plug into above equation of line is,
⇒ 3x - y = 1
⇒ 3 x 1 - 2 = 1
⇒ 3 - 2 = 1
⇒ 1 = 1
Thus, The correct point which is solution of equation of line is,
⇒ (1, 2)
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Which of the following tables represents a linear relationship that is also proportional?
Answer:
Step-by-step explanation:
proportional means the graph passes through the origin, also known as (0,0). In this case, the only table with both 0’s in the x and y is the second one from the top.
Given that abcd is a rhombus, determine the length of each diagonal, ac, and bd if m∠ade=20° and ad = 8cm. please help and show me how you did it
The length of diagonal ac is approximately 15.58 cm, and the length of diagonal bd is approximately 12.22 cm
Rhombus is a special type of parallelogram in which all four sides are congruent. The opposite angles of a rhombus are also congruent, and the diagonals bisect each other at right angles.
Now, let's consider the given rhombus abcd, where ad = 8cm and m∠ade=20°. We need to determine the length of diagonals ac and bd.
First, let's use the law of cosines to find the length of side ae. We know that ad = 8cm, and m∠ade=20°, so we can use the formula:
ae² = ad² + de² - 2ad(de)cos(m∠ade)
Substituting the values, we get:
ae² = 8² + de² - 2(8)(de)cos(20°)
Next, we can use the fact that a rhombus has all sides congruent to find the length of side de. Since abcd is a rhombus, we know that ac and bd are also congruent diagonals that bisect each other at right angles. Therefore, we can draw diagonal ac and use the Pythagorean theorem to find the length of ac:
ac² = (ae/2)² + (de/2)²
Substituting ae² from the previous equation, we get:
ac² = ((8² + de² - 2(8)(de)cos(20°))/4) + (de/2)²
Simplifying the equation and using the fact that ac and bd are congruent, we get:
bd² = ac² = (8² + de² - 2(8)(de)cos(20°))/2
Finally, we can use the Pythagorean theorem to find the length of diagonal bd:
bd² = ab² + ad²
Substituting ab = ac/2 and ad = 8cm, we get:
bd² = (ac/2)² + 8²
Substituting ac² from the previous equation, we get:
bd² = ((8² + de² - 2(8)(de)cos(20°))/8)² + 8²
Simplifying the equation, we get:
bd ≈ 12.22 cm
Similarly, we can solve for ac using the equation we derived earlier:
ac² = ((8² + de² - 2(8)(de)cos(20°))/4) + (de/2)²
Substituting de ≈ 9.84cm (which we can solve for from the equation ae² = 8² + de² - 2ad(de)cos(m∠ade)), we get:
ac ≈ 15.58 cm
Therefore, the length of diagonal ac is approximately 15.58 cm, and the length of diagonal bd is approximately 12.22 cm
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Y – 84 = -11(x – 6)
What is the point and slope
Which of the following statements is correct about the value of: 13 + √50
A. 13 + √50 is an irrational number
B. 13 + √50 is an integer
C. 13 + √50 is a rational number
D. 13 + √50 is neither a rational or irrational number
The statement that is correct about the value of: 13 + √50 is A. 13 + √50 is an irrational number
The statement that is correct about the value of: 13 + √50From the question, we have the following parameters that can be used in our computation:
13 + √50
When the above expression is evaluated we have
13 + √50 = 20.0710678119
The above result (20.0710678119) is an irrational number
This is because the number 20.0710678119 cannot be expressed as a ratio of two integers
Hence, the statement that is correct about the value of: 13 + √50 is A. 13 + √50 is an irrational number
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After Paul and Marlena got married, they decided they wanted to take a
Caribbean cruise to celebrate their ten year anniversary. The cruise will cost them
$5,800. How much should they deposit into an account now that pays 5.3%
interest, compounded daily, in order to have enough for their cruise in ten years?
A. $550.81
B. $2,431.23
C. $2,957.82
D. $3,414.04
PLEASEEE
Paul and Marlena should deposit approximately $2,431.23 into an account now to have enough for their cruise in ten years.
So, the correct answer is B. $2,431.23.
To calculate the amount Paul and Marlena should deposit into an account now in order to have enough for their cruise in ten years, we can use the formula for compound interest:
[tex]A = P(1 + r/n)^{ (nt)}[/tex]
Where:
A = the future value of the investment/loan, including interest
P = the principal amount (initial deposit)
r = the annual interest rate (in decimal form)
n = the number of times that interest is compounded per year
t = the number of years
In this case, the principal amount (P) is what we need to find.
The future value (A) is given as $5,800.
The interest rate (r) is 5.3% or 0.053 as a decimal.
The interest is compounded daily, so n = 365 (number of days in a year).
Using the formula, we can rearrange it to solve for P:
[tex]P = A / (1 + r/n)^{(nt)[/tex]
Substituting the given values:
[tex]P = 5800 / (1 + 0.053/365)^{(365\times 10)[/tex]
Calculating this expression:
P ≈ 2,431.23
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Point B is the image of point A when point A is rotated about the origin. What is known about point A and B?
Point B is the image of point A under a rotation about the origin.
Describe Rotation?Rotation is a transformation in which an object or a point is turned around a fixed point or a fixed axis. The fixed point or axis is called the center of rotation, and the angle of rotation specifies the amount and direction of the turn. When an object is rotated, its orientation changes but its shape and size remain the same.
For example, if you rotate a square by 90 degrees around its center, it will look the same as before, but it will be oriented differently. Similarly, if you rotate a point in a coordinate system around the origin, its position will change, but its distance from the origin will remain the same.
Rotations are commonly used in geometry, physics, and engineering to describe the motion of objects, such as the rotation of the Earth around its axis or the rotation of a wheel on an axle. They are also used in computer graphics to create animations and in robotics to control the movement of robotic arms and other devices.
When point A is rotated about the origin to form point B, the distance between the origin and each point remains the same. The direction from the origin to point A and the direction from the origin to point B are related by the angle of rotation. Specifically, point B is the image of point A under a rotation about the origin.
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Select the correct answer. What is the sum of the first five terms in this series? 3 + (-9) + 27 + (-81) + . . .
A. 243
B. -9
C. 61
D. 183
Pyramid A (shown below) has a volume of 20 cubic units and a height of 4 units. What is the area of its base? Rectangular pyramid Group of answer choices 80 square units 5 square units 45 square units 15 square units
The base area of the pyramid is 5 units squared.
How to find the base area?The pyramid has a volume of 20 cubic units and the height of the pyramid is 4 units.
Therefore, the area of the base can be calculated as follows:
Hence,
volume of the pyramid = base area × height of the prism
20 = base area × 4
Therefore,
base area of the pyramid = 20 / 4
base area of the pyramid = 5 units squared.
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.the function f(x) = 5^x is stretched vertically by a scale factor
of 2, shifted 3 units to the left and down 1 unit to produce the
function g(x). find g(x).
please help :d
The transformation of the function g(x) is g(x) = 250 * 5^x - 1. It represents a vertical stretch by a scale factor of 2, a shift of 3 units to the left, and a downward shift of 1 unit applied to the original function f(x) = 5^x.
- Vertical stretch by a scale factor of 2: Multiply the output by 2.
- Shift 3 units to the left: Replace x with x + 3.
- Shift 1 unit down: Subtract 1 from the output.
Thus, the function g(x) can be written as:
g(x) = 2 * f(x + 3) - 1
Substituting f(x) = 5^x, we get:
g(x) = 2 * 5^(x + 3) - 1
Simplifying:
g(x) = 2 * 125 * 5^x - 1
g(x) = 250 * 5^x - 1
The function g(x) is given by g(x) = 250 * 5^x - 1. It represents a vertical stretch by a scale factor of 2, followed by a shift of 3 units to the left, and a downward shift of 1 unit, applied to the original function f(x) = 5^x.
The transformation increases the steepness of the graph, shifts it to the left, and shifts it downward. The expression 250 * 5^x represents the vertical scaling, and the -1 accounts for the vertical shift downward. Overall, g(x) is a modified version of f(x) with these transformations applied.
Therefore, the function g(x) is g(x) = 250 * 5^x - 1.
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PLEASE HELP
A survey was done that asked people to indicate whether they prefer saltwater fishing or freshwater fish in the results of the survey are shown in the two way table
complete a relative frequency table from this data.
enter your answer is rounded to the nearest 10th of a percent in the boxes
According to the above, the fishing population is divided into 53% prefer fresh water and 47% prefer salt water.
To find the percentage of people that make up each group, we must find the total number of people who were surveyed:
228 + 245 + 242 + 285 = 1,000
Once we find the total number of people who took the survey, we can find the percentage of each value by making rules of three as shown below:
Age 30 and younger and Saltwater fishing:
1,000 = 100%
228 = ?%
Hence, We get;
228 x 100 / 1,000 = 22.8%
Age 30 and younger and Freshwater fishing:
1,000 = 100%
245 = ?%
245 x 100 / 1,000 = 24.5%
Over 30 years old and Saltwater fishing:
1,000 = 100%
242 = ?%
242 * 100 / 1,000 = 24.2%
Over 30 years old and Freshwater fishing:
1,000 = 100%
285 = ?%
285 * 100 / 1,000 = 28.5%
To find the other percentages we must find the total number of fishermen by age ranges and by fishing preference:
Age ranges
228 + 245 = 473
242 + 285 = 527
1,000 = 100%
473 = ?%
473 * 100 / 1,000 = 47.3%
1,000 = 100%
527 = ?%
527 * 100 / 1,000 = 52.3%
Fishing mode preferences
228 + 242 = 470
245 + 285 = 530
1,000 = 100%
530 = ?%
530 * 100 / 1,000 = 53%
1,000 = 100%
547 = ?%
470 * 100 / 1,000 = 47%
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A triangular frame is being built as the support for a ramp. The longest part of the
frame will sit on the ground. The second longest side is 2'3" and forms an 18°
angle with ground. The smallest side is 10" long. Determine the angle the
smallest side will make with the ground.
The smallest side of the triangle makes an angle of approximately 20.6 degrees with the ground.
To determine the angle the smallest side will make with the ground, we can use the law of sines. The law of sines states that for any triangle ABC:
a/sin(A) = b/sin(B) = c/sin(C)
where a, b, and c are the lengths of the sides opposite the angles A, B, and C, respectively.
Let's label the sides of our triangle as follows:
The longest side (sitting on the ground) is side c
The second longest side is side b
The smallest side is side a
We know that side b is 2'3" long, which is equivalent to 27 inches. We also know that side a is 10 inches long. We can use the law of sines to solve for the angle opposite side a:
sin(A) = (a/c) * sin(C)
We can solve for sin(C) by using the fact that the sum of the angles in any triangle is 180 degrees:
C = 180 - A - B
We know that angle B is 18 degrees, so we can substitute that into our equation for C:
C = 180 - A - 18
C = 162 - A
Substituting this expression for C into our equation for sin(A), we get:
sin(A) = (a/c) * sin(162 - A)
We know that c is the longest side of the triangle and therefore opposite the largest angle. Since we are interested in the angle opposite side a, we can assume that angle A is the smallest angle in the triangle. We can use this assumption to simplify our equation for sin(A):
sin(A) = (a/c) * sin(162)
Plugging in the values for a, c, and sin(162), we get:
sin(A) = (10/27) * 0.951
sin(A) = 0.352
Taking the inverse sine of both sides, we get:
A = sin^-1(0.352)
A ≈ 20.6 degrees
Therefore, the smallest side of the triangle makes an angle of approximately 20.6 degrees with the ground.
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A tennis court in the shape of a rectangle has an area of 7200 square
feet. One pair of sides measures twice the length of the other pair of
sides. What are the dimensions of the tennis court?
Answer:
60 x 120
Step-by-step explanation:
2x(x) = 7200
2[tex]x^{2}[/tex] = 7200 divide both sides by 2
[tex]x^{2}[/tex] = 3600
[tex]\sqrt{x^{2} }[/tex] = [tex]\sqrt{3600}[/tex]
x = 60
This is one of the dimensions. The other dimension is twice 60 or 120.
a = lw
a = (60)(12)
a = 7200
Helping in the name of Jesus.
3. la mamá de jordan compró 7 cajas de envases de jugo para después del entrenamiento del equipo. cada caja tenía 8 envases de jugo. después que el equipo bebió todo el jugo que quiso, quedaron 29 envases de jugo. el equipo abrió una nueva caja solo después de beber todo el jugo de la caja anterior. ¿cuántas cajas de jugo abrió el equipo?
Answer:
Step-by-step explanation:
The team drank a total of 7 x 8 = 56 juice boxes, and there were 29 remaining, so the team opened 56 - 29 = 27 juice boxes.
Since the team only opened a new box after finishing the previous one, the team opened 27 - 1 = 26 boxes of juice in total.
To explain this solution in more detail, we can use basic arithmetic. We know that the mom bought 7 boxes of juice, each containing 8 juice boxes,
so the total number of juice boxes is 7 x 8 = 56. After the team drank all the juice they wanted, there were 29 juice boxes remaining. This means that the team drank 56 - 29 = 27 juice boxes.
Since the team only opened a new box of juice after finishing the previous one, the number of boxes opened will be one less than the total number of juice boxes consumed.
Therefore, the team opened 27 - 1 = 26 boxes of juice in total. It is important to note that this assumes that the team opened all the boxes they consumed and did not drink any juice directly from the remaining boxes.
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Suppose you are doing a 5000 piece puzzle. you have already placed 175 pieces. every minute you place 10 more pieces. after 50 minutes, how many pieces will you have placed
After 50 minutes, you will have placed 675 pieces
Given, you are doing a 5000 piece puzzle. You have already placed 175 pieces, and every minute you place 10 more pieces. After 50 minutes, we need to find how many pieces you will have placed.
We can start by finding the number of pieces you place in 50 minutes.
Every minute, you place 10 more pieces, so in 50 minutes, you will place:
10 x 50 = 500 pieces
Adding the pieces you have already placed, we get:
175 + 500 = 675 pieces
Therefore, after 50 minutes, you will have placed 675 pieces
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Find f'(-2) for f(x) = ln(5x² + 20x + 1). Round to 3 decimal places, if necessary.
To find f'(-2), we need to first find the derivative of f(x) using the chain rule.
f'(x) = (1/(5x² + 20x + 1)) * (10x + 20)
Then, we can plug in x = -2 to get f'(-2):
f'(-2) = (1/(5(-2)² + 20(-2) + 1)) * (10(-2) + 20)
f'(-2) = (1/(20 - 40 + 1)) * (-20 + 20)
f'(-2) = 0
Therefore, f'(-2) is equal to 0.
To find f'(-2) for f(x) = ln(5x² + 20x + 1), we first need to find the derivative of f(x) using the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.
1. Let u = 5x² + 20x + 1. Then, f(x) = ln(u).
2. Find the derivative of f(x) with respect to u: f'(x) = d[ln(u)]/du = 1/u.
3. Find the derivative of u with respect to x: du/dx = d(5x² + 20x + 1)/dx = 10x + 20.
4. Apply the chain rule: f'(x) = (1/u) * (du/dx) = (1/(5x² + 20x + 1)) * (10x + 20).
Now, to find f'(-2), simply substitute -2 for x in the derivative:
f'(-2) = (1/(5(-2)² + 20(-2) + 1)) * (10(-2) + 20)
f'(-2) = (1/(20 - 40 + 1)) * (-20 + 20)
f'(-2) = (1/(-19)) * 0
Since any number multiplied by 0 is 0, we have:
f'(-2) = 0.000
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It has been reported that 48% of teenagers play video games on their phones. A
random sample of 60 teenages is drawn. Find the probability that the proportion of
teenagers in the sample who play videos games on their phone is less than 0. 489
The probability is less than 0.489 is approximately 0.8980 or 89.80% that the proportion of teenagers in the sample who play videos games on their phone is less than 0. 489
First, we need to calculate the mean and standard deviation of the sampling distribution of the sample proportion:
Mean = p = 0.48
Standard deviation = sqrt((p*(1-p))/n) = sqrt((0.48*0.52)/60) = 0.071
Next, we need to standardize the sample proportion using the formula:
z = (sample proportion - population proportion) / standard deviation
z = (0.489 - 0.48) / 0.071 = 1.27
Finally, we need to find the probability that the standardized sample proportion is less than 1.27 using a standard normal distribution table or calculator. This probability is approximately 0.8980.
Therefore, the probability that the proportion of teenagers in the sample who play video games on their phones is less than 0.489 is approximately 0.8980 or 89.80%.
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in each hand of a card game, there is a 54% chance of winning 3 points and a 46% chance of losing 4 points. is the game a fair game? explain
Answer: yes, the game is fair.
Step-by-step explanation:
The game is fair because:
a. you are playing with multiple players, and they have equal odds
b. the odds of winning are higher, so there is balance since you earn less points.
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W X Y Z is a kite. Find the measure of angle W.
The measure of angle W in the kite WXYZ is 0 degrees.
To find the measure of angle W in the kite WXYZ, we can use the properties of kites. In a kite, the two opposite angles formed by the intersection of the diagonals are equal. Let's denote the measure of angle W as "x."
Step 1: Start with the given information that WXYZ is a kite.
Step 2: Recall that the diagonals of a kite intersect at right angles. Let's label the intersection point of the diagonals as point P.
Step 3: Draw the diagonals WX and YZ, which intersect at point P.
Step 4: Recognize that angles WXP and ZYP are congruent. Therefore, the measure of angle WXP is also x.
Step 5: Observe that the sum of the angles in a triangle is 180 degrees. Since triangle WXP is a triangle, we can write the equation: x + 90 + 90 = 180.
Step 6: Simplify the equation: x + 180 = 180.
Step 7: Subtract 180 from both sides: x = 0.
Step 8: Analyze the result. The measure of angle W, denoted by x, is equal to 0 degrees.
Therefore, the measure of angle W in the kite WXYZ is 0 degrees.
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Select all the correct answers.
Isosceles trapezoid ABCD is shown.
Which three statements are correct?
In the given Isosceles trapezoid ABCD, the following three statements are correct:
∠ADC ≅ ∠BCD
AD ≅ BC
AC ≅ BD
An isosceles trapezoid is a trapezoid with equal base angles and hence equal left and right side lengths. Non-parallel sides on isosceles trapezoids have the same lengths. Hence, AD ≅ BC
A triangle with two equal sides is said to be isosceles. The two angles facing the two equal sides are also equal. Hence, ∠ADC ≅ ∠BCD.
The diagonals of the isosceles trapezoid are also equal. Hence, AC ≅ BD.
Thus, three correct statements in the given question are:
∠ADC ≅ ∠BCD
AD ≅ BC
AC ≅ BD
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Sam has a cylindrical storage container 7 inches tall with a radius of 5 inches.
How much cat litter will fit in the container?
Use 3. 14 for π. Round your answer to the nearest tenth.
Answer: _____________ cubic inches
The cylindrical storage container can hold 549.5 cubic inches of cat litter.
To find the volume of the cylindrical storage container, we need to use the formula:
V = πr²h
Where:
π is a constant approximately equal to 3.14
r is the radius of the container
h is the height of the container
Substituting the given values, we get:
V = 3.14 x 5² x 7
V = 549.5 cubic inches
Since we know that the vessel can hold549.5 boxy elevation of cat waste, we can use this value to determine how important cat waste can fit in the vessel in other units. For illustration, if we want to know how numerous liters of cat waste can fit in the vessel, we can convert boxy elevation to liters using the conversion factor 1 liter = 61.02 boxy elevation. boxy elevation61.02 boxy elevation per liter = 8.998 liters thus, the spherical storehouse vessel can hold roughly 9 liters of cat waste.
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A pitcher contains 13 cups of iced tea. You drink 1. 75 cups of the tea each morning
and 1. 5 cups of the tea each evening. When will you run out of iced tea?
The duration of days after which the individual will run out of iced tea is 4 days, under the condition that a pitcher can hold 13 cups of iced tea. The individual drinks 1. 75 cups of the tea every morning and 1. 5 cups of the tea each evening.
So to solve this problem we have to relie on the basic principles of division
Total amount of tea consumed per day = 1.75 cups (morning) + 1.5 cups (evening)
= 3.25 cups
Total amount of tea in the pitcher = 13 cups
Number of days before running out of iced tea = 13 cups / 3.25 cups per day
= 4 days
Then, the duration of days until the iced tea runs out is 4 days.
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A line shape like a trapezoid has an area of 337. 5ft^2 if the length of the bases are 25 fr and 20 ft then the perpendicular distance between bases would be
The perpendicular distance between the bases of a trapezoid with an area of 337.5 ft² and base lengths of 25 ft and 20 ft is 15 ft.
Area = (1/2) * (Base1 + Base2) * Height
In this case, the area is 337.5 ft², Base1 is 25 ft, and Base2 is 20 ft. We need to solve for the height, which represents the perpendicular distance between the bases.
Plugging in the known values into the formula:
337.5 = (1/2) * (25 + 20) * Height
Simplifying the expression:
337.5 = (1/2) * (45) * Height
Multiplying both sides of the equation by 2 to get rid of the fraction:
675 = 45 * Height
Dividing both sides by 45 to solve for the height:
Height = 675 / 45
Height = 15 ft
Therefore, the perpendicular distance between the bases of the trapezoid is 15 ft.
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