The total time elapsed on the astronauts' chronometers is 20 years. This is calculated by subtracting the time spent traveling to and from the distant planet (2 * 10 years = 20 years) from the total time elapsed on Earth (26 years).
This result takes into account the time dilation effect of special relativity, which states that time passes more slowly for a moving object relative to a stationary observer. Since the astronauts were traveling at high speeds for much of their journey, the time elapsed on their chronometers would be less than the time elapsed on Earth.
The total time elapsed on the astronauts' chronometers is 20 years. This is calculated by subtracting the time spent traveling to and from the distant planet (2 * 10 years = 20 years) from the total time elapsed on Earth (26 years).
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Choose all of the statements about the quadrilateral and/or the transformed quadrilateral that are correct.
A. The quadrilaterals will be congruent.
B. The quadrilateral will map onto itself.
c. The quadrilateral will now appear in Quadrant IV.
D. The quadrilaterals will have the same orientat
E. The quadrilaterals will be similar but not cong
The statements about the quadrilateral and/or the transformed quadrilateral that are correct are:
The quadrilaterals will be congruent.
Option A is the correct answer.
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
From the graph,
Quadrilateral WXYZ.
We see that,
Quadrilateral WXYZ is in the III Quadrant.
Step 1:
Rotated 180° about the origin.
This means,
Quadrilateral WXYZ is in the I Quadrant.
Step 2:
Reflection across the y-axis.
This means,
Quadrilateral WXYZ is in the II Quadrant.
Now,
Since there is no dilation the transformed quadrilateral will be congruent.
Thus,
The quadrilaterals will be congruent.
Quadrilateral WXYZ is in the II Quadrant.
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The complete question is:
Quadrilateral WXY will be rotated about the origin and then reflected across the y-axis. Choose all of the statements about the quadrilateral and/or the transformed quadrilateral that are correct.
I need help solving this
41x-2
99⁰
140⁰
The value of x based on the information about the triangle is 3.
How to calculate the value of xIt should be noted that the total sum of angles in a triangle is 180°. Based on the information given, this will be illustrated as:
180 - (180 - 140) - (180 - 99)
= 180 - 40 - 81
= 59
Therefore, 41x - 2 + 59 = 180
41x = 180 + 2 - 59
41x = 123
Divide
x = 123 / 41.
x = 3.
The value of x is 3.
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The measure of one of the small angles of a right triangle is 45 less than twice the measure of the other small angle. Find the measure of both angles
The measure of both angles is 45.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
Right triangle:
One angle = 90
Other angles:
One = 2x - 45
Another = x
Now,
The sum of the three angles = 180
90 + x + 2x - 45 = 180
Add like terms.
90 + 3x - 45 = 180
Add 45 on both sides.
90 + 3x = 180 + 45
Subtract 90 on both sides.
3x = 225 - 90
3x = 135
Divide 3 into both sides.
x = 45
Now,
Other angles:
One = 2 x 45 - 45 = 45
Another = 45
Thus,
Both angles are 45.
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the management of your team wants you to run descriptive statistics on the points scored by your team in the games played at your team's venue in 2013-2015. calculate descriptive statistics including the mean, median, variance, and standard deviation for points scored by your team played at home. make the following edits to the code block below:
in order to calculate the descriptive statistics for the points scored by the team at home in 2013-2015, the mean, median, variance and standard deviation must be calculated using the appropriate formulas.
Descriptive Statistics
Mean: This is a measure of the center of the distribution, calculated as the sum of all values divided by the number of values. In this case, it is the average number of points scored by the team at home in 2013-2015. Formula: Mean = (Sum of all values)/(Number of values).
Median: This is the middle value of the data set after it is sorted in numerical order. It is the value that separates the upper half of the data set from the lower half. In this case, it is the middle value of the points scored by the team at home in 2013-2015. Formula: Median = (Sum of the lower and upper halves of the data set)/2.
Variance: This is a measure of how spread out the data set is, calculated as the sum of the squared differences between each value and the mean, divided by the number of values. In this case, it is the variance of the points scored by the team at home in 2013-2015. Formula: Variance = (Sum of the squared differences between each value and the mean)/(Number of values).
Standard Deviation: This is a measure of how spread out the data set is, calculated as the square root of the variance. In this case, it is the standard deviation of the points scored by the team at home in 2013-2015. Formula: Standard Deviation = Square Root of Variance.
Therefore, in order to calculate the descriptive statistics for the points scored by the team at home in 2013-2015, the mean, median, variance and standard deviation must be calculated using the appropriate formulas.
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-There are some small cubes and some large cubes in a bag.
-The cubes are red or the cubes are yellow
-The ratio of the number of small cubes to the number of large cubes is 4:9
-The ratio of the number of red cubes to the number of yellow cubes is 3:5
a) What is the least possible number of cubes in the bag?
-All the small cubes are yellow.
b) Work out the least number of large yellow cubes in the bag.
The answers include the following:
The least possible number of cubes in the bag is 104.The least number of large yellow cubes in the bag is 45.What is Probability?This is referred to as the branch of mathematics concerning numerical descriptions of how likely an event is to occur,
The Red to Yellow ratio is given as 3:5.
Red = 3 to 8 and yellow = 5 to 8.
Small to Large ball ratio = 4:9
Small = 4/13 and large = 9/13
5/8 × 9 / 13 × 104
= 5 * 9
= 45
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A is four more than three times of B
Answer:
A = 3 * B + 4
Step-by-step explanation:
A - 4=3 * B (given)
A = 3 * B + 4
Do running times of American movies differ somehow from running times of French movies? The author investigated this question by randomly selecting 25 recent movies of each type, resulting in the following running times Am: 94 90 95 93 128 95 125 91 104 116 161 102 90 110 92 113 116 90 97 103 95 120 109 91 136 Fm: 123 116 90 158 122 119 125 90 96 94 137 102 105 106 95 125 122 103 96 111 81 113 128 93 92 Construct a comparative stem-and-leaf display by listing stems in the middle of your paper and then placing the Am leaves out to the left and the Fr leaves out to the right. (Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values.) American Stems French 10 12 13 14 15 16 Comment on interesting features of the display. (Select all that apply.) French movies are unimodal strongly positively skewed, while American movies appear to be bimodal American movies are unimodal strongly positively skewed, while French movies appear to be bimodal. O A typical French movie runs around 95 minutes, while American movies are typically either around 95 minutes or around 125 minutes
The results of this investigation provide valuable insights into the differences in the film-making practices of American and French film industries.
The comparative stem-and-leaf display is as follows:
90 | AM: 90 90 91 92 94 95 95 95 97 NONE
91 | AM: 104 110 113 113 116 116 116 120 125
92 | AM: 128 136
95 | FM: 90 95 96 97 102 103 105 106 111 113 113 125 125 128 158
96 | FM: 90 94 96
97 | NONE
102 | FM: 102
103 | AM: 103
104 | AM: 104
105 | FM: 105
106 | FM: 106
109 | AM: 109
110 | AM: 110
111 | FM: 111
113 | AM: 113
116 | FM: 116 122 123
120 | AM: 120
125 | FM: 125
128 | FM: 128
136 | AM: 136
158 | FM: 158
The display shows that American movies appear to be bimodal, with a typical running time of around 95 minutes and another peak around 125 minutes. On the other hand, French movies are unimodal and strongly positively skewed with a typical running time of around 95 minutes. This suggests that French movies tend to have a shorter running time compared to American movies, but with a larger range of running times compared to the peak of American movies around 95 minutes.
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What shape is the cross-section?
(it isnt a multiple choice question sorry)
The shape of the cross section is Trapezium.
What is Cross- Section?A cross-section is a shape that results from the cutting of a solid (such as a cone, cylinder, or sphere) by a plane.
For instance, if the base of a cylinder-shaped object is cut by a plane, the resulting cross-section will be a circle.
Given:
Here we have the figure of shape Triangular Pyramid.
and, the plane cutting the Pyramid is in shape of square.
So, the resultant cross section will be of the shape as seen from the cutting is Trapezium.
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If the force acting on an object stays the same, then the acceleration of the object varies inversely as its mass. If an object with a mass of 27 kilograms accelerates at a rate of 2 meters per second per second by a force, find the rate of acceleration of an object with a mass of 3 kilograms that is pulled by the same force.
The rate of acceleration of an object with a mass of 3 kilograms that is pulled by the same force is given as follows:
18 m/s².
What is the relation between force, mass and acceleration?According to Newton's Second Law, the force is given by the multiplication of the mass and of the acceleration, as follows:
F = ma.
The force is obtained as follows, considering a mass of 27 kg and an acceleration of 2 m/s².
F = 27 x 2
F = 54N.
Then the acceleration of an object of 3 kilograms with the same force is given as follows:
3a = 54
a = 54/3
a = 18 m/s².
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In the given figure, mHK = 50° and m/GKL = 50°.
Which statement is true?
The measure of ZJ is 25°, and triangle JKG is isosceles.
The measure of ZJ is 50°, and triangle JKG is isosceles.
The measure of ZJ is 25°, and triangle JKG is not isosceles.
The measure of ZJ is 50°, and triangle JKG is not isosceles.
Answer:
Step-by-step explanation:
The answer is A have a nice day :)
Cigarette Taxes The increases (in cents) in cigarette taxes for 17 states in a 6-month period are 60, 20, 40, 40, 45, 12, 34, 51, 30, 70, 42, 31, 69, 32, 8, 18.50 )g Find the range, variance, and standard deviation for the data. Use the range rule of thumb to estimate the stand- ard deviation. Compare the estimate to the actual stand- ard deviation.
The graph shows the position (distant from home) of a bicycle rider on a 42-minute trip. Letters A through E are time intervals during the trip. The key defines the length of each interval.
Use the equation below to calculate the bicycle rider’s average speed in kilometers per minute for the first 30 minutes of the trip
Distance(km)/time(min) = average speed
The average speed on the first 30 minutes is 0.2 km per min.
How to get the average speed?Here we have the graph for the position of a bycicle rider on a 42-minute trip.
On the vertical axis we can see the position, and on the horizontal axis we can see the time.
Remember that:
speed = distance/time.
To find the average speed on the first 30 min, we need to take the quotient between the position after 30 minutes and 30 min.
At 30 min we can see that the position is at 6 km, then the speed will be:
S = 6km/30min = 0.2 km per min.
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Factor 48-6 using GCF
Answer:
I think the answer is six i just searched it or it could be 12
Step-by-step explanation:
The greatest common factor (GCF) of 48 and 6 is 6, so:
48 - 6 = 42.
this isn't college level *laugh*
In the function P(t) = 309.3 . 1.008', P represents the population in millions and represents the number of years since 2010. Find the population in 2019 and the rate at which the population is growing in 2019. Use h = 0.001 to estimate the derivative with the difference quotient. The population in 2019 is !! million. The rate at which the population is growing in 2019 is million people per year. (Round answers to three decimal places.) Hint: The population in 2019 is P(9). The rate of change in 2019 is P' (9).
The population in 2019 is 311.8 million and the rate of change of the population in 2019 is 0.083 million people per year.
To find the population in 2019 and the rate at which the population is growing in 2019, we can use the given function P(t) = 309.3 . 1.008. Here, P represents the population in millions and t represents the number of years since 2010. We can use the difference quotient to estimate the derivative. The difference quotient for this function is (P(t+h)-P(t))/h where h is the difference in the number of years. For this question, h = 0.001. The population in 2019 is P(9) = 309.3 . 1.008^9 = 311.8 million people. The rate of change in 2019 is P' (9), which is calculated using the difference quotient. This comes to (P(9+0.001)-P(9))/0.001 = (311.811 - 311.8)/0.001 = 0.083 million people per year.
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I need Help on this question.
The equation that represents "triple the input, then subtract 5" will be written as y = 3x - 5.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The output is less than 5 to 3 times the input.
Let 'x' be the input and 'y' be the output. Then the equation is given as,
y = 3x - 5
The equation that represents "triple the input, then subtract 5" will be written as y = 3x - 5.
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each of the following three data sets represents the iq scores of a random sample of adults. iq scores are known to have a mean and median of 100.
a) The mean of the sample of size 5 is equals to 103.
b) The mean of the sample of size 12 is equals to 103.3.
c) Median of sample of size 5 is 104.
d) Median sample of size 30 is 105.5.
Mean: Sum of observations is divided by number of observations in the sample is named as mean, which is denoted by X- bar. Moreover, the sample mean signifies the measure of centre of the data.
X-bar = (x₁ + x₂ + --- + xₙ)/n
Median: Median divides the observations into two equal parts. It represents the middle value for a set of observations when they are arranged in order of magnitude. There are two cases arises.
Case (1): Sample size (n) is odd: First, arrange the data in ascending order. Then, the median is the middle value and lies at the position.
Case (2): Sample size (n) is even: First, arrange the data in ascending order. Then, the median is the mean of the two data values that lie on either side of the position. Median = ( n/2)ᵗʰ term , n is odd
=[(( n/2)ᵗʰ term + (n/2 + 1)ᵗʰ term]/2, n is even
Now, a) Mean of first sample with sample size, n = 5.
Sum of values = 105 + 111 + 97 + 94 + 108 = 515
So, mean = 515/5 = 103
b) Sample 2, sample size , n = 12
Sum of values = 105 + 111 + 97 + 94 + 108 + 101 + 112 + 114 + 103+ 102+ 91 + 101
= 515 + 724 = 1239
Mean = 1239/12 = 103.25
c) Now, we have to determine median for sample size 5. Here, sample values are odd in number, i.e., 5. So, middle term is median after arranging in order. Ascending order is 94,97, 104, 108, 111 and middle term is 104, so median is 104.
d) Now, we have a sample of size 30, which is an even number. First arrange the numbers in ascending order as 91,92,92,94,95,97,100,101,101,101,101,102,103,105,105,105,106,107,107,108,110,111, 111, 112,113,114,115,115,116,116. So,
Median is [((n/2)th + (n/2 + 1)th ]/2 i.e, [ 30/2)th + 30/2 + 1)th ]/2
=( 15th + 16th)/2 ( observations)
= (105 + 106 )/2 = 211/2 = 105.5
Hence, the median of sample size 30 is 105.5.
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Complete question:
See the above figure, each of the following three data sets represents the iq scores of a random sample of adults. iq scores are known to have a mean and median of 100.
a) What is the mean of the sample of size 5? Full data set Sample of Size 108 114 (Type an integer or decimal rounded to one decimal place as needed._ Sample of Size 12
b) What is the mean of the sample of size 12? 114 105 115 (Type an integer or decimal rounded to one decimal place as needed:)
c) What is the median of the sample of size 5? (Type an integer or decimal rounded to one decimal place as needed:)
d) What is the median of the sample of size 30? (Type an integer or decimal rounded to one decimal place as needed:)
As you were orginizing your closet you counted 20 shirts and 12 pairs of pants what was the pants to shirts ratio
The ratio of the given distribution of pants to shirts is; 5:3
How to solve ratio problems?The ratio of shirts to pants can be expressed by putting the number of shirts and pants in the following way;
Number of shirts : Number of pants
20 : 12
Then we will have to reduce this ratio to the lowest term by dividing by the highest common factor of both numbers.
The highest common factor of 12 and 20 is 4 and as such when divided by 4 we get:
20/4 : 12/4
= 5 : 3
This represents the ratio.
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An aerospace engineering student performs an experiment in a wind tunnel to determine the lift coefficient of an airfoil. The student takes 61 measurements of the vertical force using a force balance, yielding a sample mean value of 44.20 N and a sample variance of 4.00 N^2. Determine (a) the percent probability that an additional measurement will be between 45.56 N and 48.20 N, (b) the range (in N) over which the true mean value will be, assuming 90 % confidence, and (c) the range (in N^2) over which the true variance will be assuming 90 % confidence.
The mean of these five values is 9.6. This means that the average value of the five numbers is 9.6.
The formula for calculating the mean is:
Mean = (Sum of all values) / (Number of values)
For example, if you had the following numbers: 4, 8, 10, 12, and 15, you would calculate the mean by adding the values together and then dividing by the number of values:
Mean = (4 + 8 + 10 + 12 + 15) / 5 = 9.6
The mean of these five values is 9.6. This means that the average value of the five numbers is 9.6.
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diameter of a circle is 13 ft. Find its circumference in terms of pi
Answer:
Step-by-step explanation:
C= 2pi
15= diameter. Radius= 13/2. R= 7.5
C= 2 times pi times 7.2
C=13 pi
C= 47.1
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Carmen went rock climbing at the climbing gym for 1
1
2
hours on Thursday. On Saturday, she went to Castle Rock State Park and climbed for 1
1
2
times as long. How much time did she spend rock climbing in all?
The total time taken by Carmen in climbing the rocks will be 2¹/₄ hours.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Carmen went rock climbing at the climbing gym for 1¹/₂ hours on Thursday. On Saturday, she went to Castle Rock State Park and climbed for 1¹/₂ times as long.
The total time of climbing will be calculated as:-
Time = 1¹/₂ x 1¹/₂
Time = ( 3 / 2 ) x ( 3 / 2 )
Time = 9 / 4
Time = 2¹/₄ hours.
Hence, the climbing time would be 2¹/₄ hours.
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The midpoints of the three sides of a triangle are P(-7; -2), Q(-1; 9) and R(5; -3).
Calculate the area of the circumscribed circle of the triangle.
Therefore , the solution of the given problem of area comes out to be Area of circle 85π cm2.
Describe surface areaIts surface area provides a good estimate of its overall size. When computing a right triangle's squared, the surroundings are taken into consideration. The surface area of everything determines its overall size. The sum of the volumes on each of the six horizontal sides makes up the volume of water inside a cuboid. Utilize the following formula to get the box's dimensions: In 2lh, 2lw, and 2hw, the region is the same (SA). The flexible shape's total area serves as a representation of the area.
Here,
Given:
Points :P(-7; -2), Q(-1; 9) and R(5; -3).
The area of the circumscribed circle of the triangle.
is:
=> PQ = √(-7 - (-1))² + (-2 - (-9))²
=> PQ = √85
The radius is √85
=> Area of circle = π(√85)²
=> Area of circle = 85π cm2
Therefore , the solution of the given problem of area comes out to be Area of circle : 85π cm2.
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If a population has mean 100 and standard deviation 20, what is the mean of the sampling distribution of sample size n = 252 b. If a population has mean 100 and standard deviation 20, what is the standard deviation of the sampling distribution of sample size n = 25? 4 c. A given exam has a normal distribution with a mean of 70 and a standard deviation of 10. A sample of size 25 is selected. What percentage of the time would you expect the mean of this sample size to fall between 66 and 74? d. A given exam has a normal distribution with a mean of 70 and a standard deviation of 10. A sample of size 25 is selected. What percentage of the time would you expect the mean of this sample size to be less than 70? % e. A given exam has a normal distribution with a mean of 70 and a standard deviation of 10. A sample of size 25 is selected. What percentage of the time would you expect the mean of this sample size to be greater than 68? %
The percent of the time you would expect the mean of the sample size of 25 to fall between 66 and 74 is 68.27%, to be less than 70 is 50%, and to be greater than 68 is 84.13%.
a. If a population has a mean of 100 and a standard deviation of 20, then the mean of the sampling distribution of a sample size of n=252 will be 100. This is because the sample means of a sampling distribution will always be equal to the population mean.
b. The standard deviation of the sampling distribution of a sample size of n=25 is 4. This is calculated using the formula: σx = σ/√n, where σ is the population standard deviation (20) and n is the sample size (25).
c. The percentage of the time you would expect the mean of the sample size to fall between 66 and 74 is 68.27%. This is calculated using the Z-score formula, which is (x-μ)/σ, where x is the upper limit (74), μ is the population mean (70), and σ is the population standard deviation (10). The Z-score for the upper limit is (74-70)/10=0.4. We then use the standard normal table to find the area between -∞ and 0.4, which is 0.6827.
d. The percentage of the time you would expect the mean of the sample size to be less than 70 is 50%. This is because the Z-score for a mean of 70 is 0, and the area below 0 is 0.5 or 50%.
e. The percentage of the time you would expect the mean of the sample size to be greater than 68 is 84.13%. This is calculated using the Z-score formula, which is (x-μ)/σ, where x is the lower limit (68), μ is the population mean (70), and σ is the population standard deviation (10). The Z-score for the lower limit is (68-70)/10=-0.2. We then use the standard normal table to find the area between -∞ and -0.2, which is 0.8413.
The percent of the time you would expect the mean of the sample size of 25 to fall between 66 and 74 is 68.27%, to be less than 70 is 50%, and to be greater than 68 is 84.13%.
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a) is y=3/2x proportional and what is the constant of proportionality ?
b) is -x=y proportional and what is the constant of proportionality
Answer:
In y = 3/2x, x and y are inversely propotional
In -x = y, x and y are directly propotional
Step-by-step explanation:
In y = 3/2x, the constant of propotionality is 3/2.
In -x = y, the constant of propotionality is -1.
Below are two inequalities and the graphs of their lines without the shading. By
imagining where the shading should be, identify which point would satisfy BOTH
inequalities.
y<-5/6x+2
y>1/3x+3
Shaded region is between the lines corresponding to both inequalities.
Point that satisfy both inequalities is (-6/7 , 19/7)
What is inequality?Inequalities are the mathematical expressions in which both sides are not-equal. In inequality, unlike in equations, we compare two values.
Given inequalities
y<(-5/6)x+2
equation of the line becomes
y = (-5/6)x + 2 ------(1)
y>(1/3)x+3
equation of the line becomes
y = (1/3)x + 3 --------(2)
By the inequalities
(1/3)x + 3 < y < (-5/6)x + 2
shaded region should be between the lines.
Solving equation 1 and 2
(-5/6)x + 2 = (1/3)x + 3
(-5/6)x - (1/3)x = 3 - 2
(-5 - 2)x/6 = 1
-7x = 6
x = -6/7
Putting value of x in equation 2
y = (1/3)(-6/7) + 3
y = -2/7 + 3
y = (-2 + 21)/7
y = 19/7
Point is (-6/7 , 19/7)
Hence, point that satisfy both inequalities is (-6/7 , 19/7),
shaded region is between both lines corresponding to the inequalities.
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Which best describes the solution set for the inequality below?
3x + 7 ≤4x-8 or-2x + 3≥1
Ox≤1or x ≥ 15
Ox≥1 orx≤ 15
Ox≥1
Ox≤ 15
The solution for the given inequalities is x≥15 or x≤1. Therefore, option A is the correct answer.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The given inequalities are 3x + 7 ≤ 4x-8 or-2x + 3≥1.
Here, 3x + 7 ≤ 4x-8
Subtract 3x on both the sides of an inequality, we get
7 ≤ x-8
Add 8 on both the sides of an inequality, we get
15≤ x
x≥15
Here, -2x + 3≥1
Subtract 3 on both the sides of an inequality, we get
-2x≥-2
Divide -2 on both the sides of an inequality, we get
x≤1
So, x≥15 or x≤1
Therefore, option A is the correct answer.
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6th grade math please help (only answer if you know the answer don't guess PELASEE) Marking brainlist!! QUESTION WORTH 60 POINT!!
Which ordered pair represents the point labeled as G?
negative one-half, one and one-fourth
three-fourths, three-fourths
0, negative one and one-fourth
negative one and one-fourth, negative one-half
Answer:
negative one and one-fourth, negative one-half
Step-by-step explanation:
it seems to be the only possible answer because the y value is negative one half
Answer: negative one and one-fourth, negative one-half
You deposit $1000 into an account that pays interest compounded monthly. What interest rate do you need to double your money in 10 years? (as a percent, so change it back, write to two decimal places)
The interest rate required to double your money in 10 years with monthly compounding is approximately 133.27%.
How did we get the value?To calculate the interest rate required to double your money in 10 years with monthly compounding, you can use the formula:
rate = ( (2 * principal) / principal * (1 + n)^(t12) )^(1/t12) - 1
where
principal = $1000
t = 10 years
n = number of compounding periods per year (12 for monthly compounding)
Plugging in the values we get:
rate = ( (2 * 1000) / 1000 * (1 + 12)^(1012) )^(1/1012) - 1
rate = ( 2 * (1 + 12)^120 )^(1/120) - 1
rate = ( 2 * 169860981.54 )^(1/120) - 1
rate = 1.3327
So, the interest rate required to double your money in 10 years with monthly compounding is approximately 133.27%.
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a series is given by 131+232+333+434+535+.... francine correctly applies the ratio test to determine whether the series converges or diverges. which statement reflects francine's conclusion?
A series is given by 131+232+333+434+535+.... francine correctly applies the ratio test, the statement that reflects francine's conclusion is From the ratio test, r=1/3. The series converges.
We must calculate the ratio between two successive phrases in order to perform the ratio test:
The nth term is n / 3n.
The (n + 1)th term is (n + 1) / 3n + 1.
The ratio test: lim | [ (n + 1) / 3n + 1 ] / [ n / 3n ] |
= lim | [ (n + 1) / n ] · [ 3n / 3n + 1 ] |
= lim | [ (n + 1) / n ] · [ 1/3 ] |
= (1/3) · lim | (n + 1) / n |
= (1/3) · lim | ( n/n ) + (1/n) |
= (1/3) · lim | 1 + (1/n) |
= (1/3) · [ lim | 1 | + lim | 1/n |
= (1/3) · [ 1 + 0 |
According to the ratio test, the series converges if this ratio is between -1 and 1 (excluded). This sequence thus comes together.
= (1/3) <--- converges
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Answer:
From the ratio test, r=13. The series converges.
Step-by-step explanation:
I took the Test
A bag of garden soil weighs 40 pounds and holds 2 cubic feet. Find the weight of 15 bags in kilograms and the volu
of 15 bags in cubic yards.
The weight of 15 bags in kilograms and the volume of 15 bags in cubic yards are 272. 15 kilograms and 1. 1 cubic yards
How to determine the valuesIt is important to note the conversion rate of the pounds to kilograms and also cubic feet to cubic yards
1 pound = 0. 453592 kilogram
If a bag of soil weighs 40 pounds which is equivalent to 0. 453592 kilogram
1 bag = 40(0.453592)
15 bags = x
x = 272. 15 kilograms
Then, we have that;
1 bag = 2 cubic feet
15 bags = 30 cubic feet
But, 1 cubic feet = 0. 037037 cubic yards
30 cubic feet = x
x = 1. 1 cubic yards
Hence, the values are 272. 15 kilograms and 1. 1 cubic yards
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4. Computing costs to rent an LCD projector. Cesar is renting an LCD projector. The rental company charges a $10 flat fee for administrative costs plus $18 per day for the projector. If Cesar
had a bill of $82, how many days did he keep the projector?
If Cesar had a bill of $82 for renting an LCD projector, he kept the projector for 4 days, based on the linear equation.
How the number of days are determined?To determine the number of days the projector, we deploy linear equation, which is in the form of y = mx + b, where m is the slope, x and y are variables, and b is the y-intercept.
The flat fee for administrative costs = $10
The variable cost per day = $18
The total bill for renting the projector = $82
The number of days = x
Linear Equation:10 + 18x = 82
18x = 72
x = 4
Check:
10 + 18x = 82
10 + 18(4) = 82
10 + 72 = 82
82 = 82
Thus, setting a linear equation, we can determine the number of days the projector was rented as 4 days.
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