The school budget for e-readers was $40,000 in 2014. The budget for 2015 was 20% less than the budget for 2014. What was the school budget for e-readers in 2015?
Answer: 32000
Step-by-step explanation: 40000 x 80% because you still have 80 percent of that budget so you minus 20 for 100.
HELP! In order to graduate from Ohio, you need to earn 3 points on an Algebra EOC or score remediation
free scores on the ACT and SAT math exams. The EOC exams are normally distributed with a mean of 703. 27
and a standard deviation of 34. 14. A score of 700 is needed to earn 3 points
To find the probability of scoring at least 700 points on the Algebra EOC, we calculate the z-score, which is -0.122, and then find the area under the standard normal curve using a z-table. The probability is 54.98%. Since this is higher than the significance level of 0.05, we can conclude that the student has met the requirement to earn 3 points on the EOC.
Identify the mean, standard deviation, and score needed to earn 3 points
Mean (μ) = 704.39
Standard deviation (σ) = 36.18
Score needed for 3 points = 700
Calculate the z-score for the score needed to earn 3 points
z = (score - μ) / σ
= (700 - 704.39) / 36.18
= -0.122
Look up the area to the left of the z-score in the standard normal distribution table
The area to the left of -0.122 is 0.4502.
Subtract the area found in step 3 from 1 to find the area to the right of the z-score
Area to the right = 1 - 0.4502 = 0.5498
Convert the area to the right into a percentage
Percentage = 0.5498 x 100% = 54.98%
Interpret the percentage as the probability of earning 3 points or more on the Algebra EOC exam:
The probability of earning 3 points or more on the Algebra EOC exam is 54.98%.
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--The given question is incomplete, the complete question is given
" In order to graduate from Ohio, you need to earn 3 points on an Algebra EOC or score remediation
free scores on the ACT and SAT math exams. The EOC exams are normally distributed with a mean of 704.39
and a standard deviation of 36.18. A score of 700 is needed to earn 3 points.
a. Fill in the values of each standard deviation above and below the mean, and make sure to add in the value
of the mean. Answers only are fine. "--
A movie ticket is 12.00 plus an 8.5 sales tax how much will one ticket movie cost
The cost of one movie ticket, including sales tax, is $13.02
The cost of the movie ticket is $12.00, and the sales tax rate is 8.5%. To find the amount of sales tax on the ticket, we can multiply the ticket price by the tax rate:
Sales tax = 12.00 * 0.085
= 1.02
So the sales tax on the ticket is $1.02.
To find the total cost of the ticket, we add the ticket price to the sales tax:
Total cost = 12.00 + 1.02
= 13.02
Therefore, the cost of one movie ticket, including sales tax, is $13.02.
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What is the surface area of this right triangular prism?
The surface area of the triangular prism is 720in²
What is surface area of prism?A prism is a solid shape that is bound on all its sides by plane faces.
The surface area of a prism is expressed as
SA = 2B +ph
where p is the perimeter of the base and h is the height of the prism.
Base area = 1/2 bh
= 1/2 × 24 × 5
= 12 × 5
= 60 in²
Perimeter of the base = 24 +13 +13
= 50 in²
the height of the prism = 12 in
therefore SA = 2 × 60+ 12 × 50
= 120 + 600
= 720 in²
Therefore the surface area of the prism is 720 in²
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I just need the answer to question 3
Answer:46.15% or rounded 46% of pulling a card higher than 8.
Step-by-step explantwenty. Well there are 6 cards higher than 8, which include 9, 10, jack, queen, king, and ace. There is 4 diffrent suites so do 6×4=24. Then do 24/52=0.4615
Answer: 46.15%
Write a number that is greater than 10,910,099,999 but less than 11,000,000,000
Answer: 10, 911,000,000
Step-by-step explanation:
10,911,000,000 < 11,000,000,000
10,911,000,000 > 10,910,099,999
i need help fast look at photo
Step-by-step explanation:
B
26 = 13.5 + m/2.5; m = 31.25
26 = 13.5 + 31.25/2.5
26 = 13.5 + 12.5
26 = 26
What are the common factors or 12 and 42
2, 3 are the common prime factors of 12 and 42.
Use the drawing tool(s) to form the correct answer on the provided graph.
Plot the axis of symmetry and the vertex for this function: h(x) = (x − 5)2 − 7
A graph of the axis of symmetry and the vertex for this function is shown below.
What is the graph of a quadratic function?In Mathematics and Geometry, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. Based on the graph of this quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0).
Since the leading coefficient (value of a) in the given quadratic function h(x) = (x - 5)² - 7 is positive 1, we can logically deduce that the parabola would open upward and the solution would be on the x-intercepts. Also, the value of the quadratic function f(x) would be minimum at -7.
In conclusion, the turning point and vertex is given by the ordered pair (5, -7).
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what is the distinction between a positive and negative mean deviation in terms of meaning applied to the data values?
Positive mean deviation means that the data values are on average greater than the mean, while negative mean deviation means that the data values are on average lower than the mean. This provides insight into the distribution of the data and can help identify outliers or trends in the data.
Mean deviation is a measure of dispersion that indicates how much a set of data values varies from the mean value of the data set. A positive mean deviation indicates that the data values are larger than the mean value, while a negative mean deviation indicates that the data values are smaller than the mean value.
In other words, a positive mean deviation indicates that the data set tends to be higher than the average, while a negative mean deviation indicates that the data set tends to be lower than the average.
Therefore, the sign of the mean deviation reflects the direction of deviation of the data values from the mean value, whether above or below it, and it provides important information about the distribution of the data set.
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1. deagan is painting a mural of a triangle for a lwhs conference room. the
triangular-shaped mural will be a total of 289 square feet; the height is 25
feet. what is the measure ofthe base?
question involving a mural painted by Deagan, which features a triangle, for a conference room at LWHS. You'd like to know the measure of the base.
Unfortunately, it seems that some essential information is missing from your question, such as the dimensions or other properties of the triangle. In order to accurately answer your question and calculate the measure of the base, please provide more information about the triangle or any related information given in the problem.
Once you provide the necessary information, I'd be happy to help you find the measure of the base and explain the process step-by-step!
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4. What is the difference in the radii of the circles? (3 points) (this is for the ana circle question
The difference between the radii of the two circular tracks is 15ft
How do we calculate?The total length of track 1 is 220ft, which means that the circumference of the circle is 220ft
we find the diameter of each track.
The circumference of a circle can be found using the formula
P = πd
d = P /π
track 1, we have
d1 = P1 / π
d1 = 220 / π
d1 = 70.03 ft.
track 2, we have
d2 = P2 / π
d2 = 126 / π
d2 = 40.11 ft.
radius of tract 1 = 35.01 ft
radius of track 2 = 20.05 ft
The difference between the two track radius is
∆r = r1 - r2
∆r = 110 / π - 63 / π
∆r = (110 - 63) / π
∆r = 47 / π
∆r = 14.96 ft.
∆r = 15 ft
In conclusion, difference between the radii of the two circular tracks is 15ft
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#complete question:
What is the difference between the radii of the two circular tracks? Answer the questions to find out.
1. Are the distances of 220 feet and 126 feet the radii, diameters, or circumferences of the two circles?
The rule is x→y=−2x. Can you mark all the points that fit the rule on a coordinate plane?
Yes, the points that fit the rule x→y=−2x can be plotted or marked on a coordinate plane, and will form a straight line passing through the origin with a slope of -2.
The rule x→y=−2x means that for every value of x, the corresponding value of y is equal to -2 times x. To plot the points that fit this rule, we can choose some values of x, substitute them into the equation, and then plot the resulting points on the coordinate plane.
For example, if we choose x=1, then y=−2x=−2(1)=−2. So the point that fits the rule is (1, −2). Similarly, if we choose x=2, then y=−2x=−2(2)=−4. So the point that fits the rule is (2, −4).
We can continue this process for other values of x, and plot all the resulting points on the coordinate plane. The resulting graph will be a straight line that passes through the origin, with a slope of -2. This means that all the points that fit the rule will lie on this line.
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The point at which a company's costs equal its revenues is the break-even point. C represents the cost, in dollars, of x units of a product and R represents the revenue, in dollars, from the sale of x units. Find the number of units that must be produced and sold in order to break even. That is, find the value of x for which C=R.
C=15x +300 and R=17.5x.
Question content area bottom
Part 1
How many units must be produced and sold in order to break even?
The number of units that must be produced and sold in order to break even = 120
Consider equation C = 15x +300
This equation represents the cost, in dollars, of x units of a product
and equation R = 17.5x represents the revenue, in dollars, from the sale of x units.
In order to find the number of units that must be produced and sold in order to break even, consider C = R
i.e., 15x + 300 = 17.5x
We solve this equation for x.
17.5x - 15x = 300
(17.5 - 15)x = 300
2.5x = 300
x = 300/(2.5)
x = 120
This is the required number of units.
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Your doing practice 6
Answer:
A ∪ B = {1, 2, 3, 4, 5, 6, 7, 9}
Step-by-step explanation:
We can find the union of two sets by including all of the numbers in both sets, but without repeating any numbers.
For example:
if A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7, 8},
then A ∪ B = {1, 2, 3, 4, 5, 6, 7, 8}
We can apply this concept to the problem at hand, but first we need to represent set A as a list of numbers:
They all have to be odd numbers between 0 and 10.
[tex]\implies A[/tex] = {1, 3, 5, 7, 9}
We are given that B = {2, 3, 4, 5, 6}. So, to find the union of A and B, we can combine both sets of numbers and get rid of copies:
A ∪ B = {1, 2, 3, 4, 5, 6, 7, 9}
You rent an apartment that costs $1600$1600 per month during the first year, but the rent is set to go up 12.5% per year. What would be the rent of the apartment during the 10th year of living in the apartment? Round to the nearest tenth (if necessary).
The rent of the apartment during the 10th year of living in the apartment would be $4940.79
To solve the problem, we need to use the formula for compound interest:
A = P * (1 + r/n)^(n*t)
where:
A is the final amount
P is the initial principal
r is the annual interest rate (as a decimal)
n is the number of times the interest is compounded per year
t is the number of years
In this case, the "principal" is the initial rent of $1600 per month, and the "interest rate" is the 12.5% increase per year. We want to find out the rent during the 10th year, so t = 10.
Let's plug in the values and solve for A:
A = 1600 * (1 + 0.125/12)^(12*10)
A = 1600 * (1.01042)^120
A = 1600 * 3.086
A = 4940.79
So the rent during the 10th year would be $4940.79 per month, rounded to the nearest tenth.
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Calculate the expected count for women who suffer from depression and drink between 2-6 cups of caffeinated coffee per week under the null hypothesis. calculate the contribution of the cell for women who suffer from depression and drink between 2-6 cups of caffeinated coffee per week to the chi-square test statistic.
The cell for women who suffer from depression and drink between 2-6 cups of caffeinated coffee per week contributes 4 to the overall chi-square test statistic.
To calculate the expected count for women who suffer from depression and drink between 2-6 cups of caffeinated coffee per week under the null hypothesis, you would first need to determine the overall proportion of women who suffer from depression and drink between 2-6 cups of caffeinated coffee per week in the sample. Let's say this proportion is 0.20.
Next, you would multiply this proportion by the total sample size to get the expected count. Let's say the total sample size is 500 women. The expected count for women who suffer from depression and drink between 2-6 cups of caffeinated coffee per week would be:
Expected count = 0.20 x 500 = 100
To calculate the contribution of the cell for women who suffer from depression and drink between 2-6 cups of caffeinated coffee per week to the chi-square test statistic, you would need to subtract the expected count from the observed count for this cell, square the difference, and divide by the expected count. Let's say the observed count for this cell is 80.
Contribution to chi-square = (80 - 100)^2 / 100 = 4
This means that the cell for women who suffer from depression and drink between 2-6 cups of caffeinated coffee per week contributes 4 to the overall chi-square test statistic.
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Include all given digits mercury venus earth mars jupiter saturn uranus neptune distance from the sun (au) 0. 39 0. 72 1 1. 52 na 19. 18 30. 06 orbital period (years) 0. 242 0. 0616 1 1. 88 na 84. 0 165
The values of distance and orbital periods of planets Mercury is 0.39AU and 0.242yrs,Venus 0.72AU distance and 0.616yrs,Earth 1AU distance and 1yrs,Mars 1.52AUdistance and 1.88,Jupiter 5.2AUdistance and 1.88 ,Saturn N/Adistance and NA years as infromation is not provided,Uranus 19.18AUdistance and 84yrs,Neptune 30.06AUdistance and165yrs.
Based on the given information, here are some key facts about the planets in our solar system:
- Mercury is the closest planet to the Sun, with a distance from the Sun of 0.39 astronomical units (AU). It has an orbital period of 0.242 years.
- Venus is the second planet from the Sun, with a distance of 0.72 AU. Its orbital period is 0.616 years.
- Earth is the third planet from the Sun, with a distance of 1 AU. Its orbital period is 1 year.
- Mars is the fourth planet from the Sun, with a distance of 1.52 AU. Its orbital period is 1.88 years.
- Jupiter is the fifth planet from the Sun, with a distance of 5.2 AU. Its orbital period is 11.86 years.
- Saturn is the sixth planet from the Sun, with a distance of N/A AU. Its orbital period is N/A.
- Uranus is the seventh planet from the Sun, with a distance of 19.18 AU. Its orbital period is 84 years.
- Neptune is the eighth planet from the Sun, with a distance of 30.06 AU. Its orbital period is 165 years.
Therefore the the distance and orbital periods are in increasing arrangement mercury, venus, earth, mars, jupiter, saturn ,uranus, neptune distance from the sun.
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A random sample of size n 1 equals 31 results in a sample mean of 123. 3 and a sample standard deviation of 8. 5. An independent sample of size n 2 equals 50 results in a sample mean of 129. 8 and sample standard deviation of 7. 3. Does this constitute sufficient evidence to conclude that the population means differ at the alpha equals 0. 01 level of significance?
The basketball coach can order approximately 34 shooting shirts for $300.
To determine the number of shooting shirts the basketball coach can order for $300, we need to solve the equation C = 0.2x^2 + 1.6x + 15, where C represents the cost and x represents the number of shooting shirts.
The equation is given as C = 0.2x^2 + 1.6x + 15.
To find the number of shooting shirts for $300, we set the cost C equal to 300 and solve for x:
0.2x^2 + 1.6x + 15 = 300
0.2x^2 + 1.6x + 15 - 300 = 0
0.2x^2 + 1.6x - 285 = 0
Now we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
For this equation, a = 0.2, b = 1.6, and c = -285. Plugging in these values into the quadratic formula:
x = (-1.6 ± sqrt(1.6^2 - 4 * 0.2 * -285)) / (2 * 0.2)
Simplifying the equation further:
x = (-1.6 ± sqrt(2.56 + 228)) / 0.4
x = (-1.6 ± sqrt(230.56)) / 0.4
x = (-1.6 ± 15.18) / 0.4
Now we have two solutions:
x1 = (-1.6 + 15.18) / 0.4 = 33.95
x2 = (-1.6 - 15.18) / 0.4 = -44.95
Since the number of shooting shirts cannot be negative, we discard the negative solution.
Therefore, the basketball coach can order approximately 34 shooting shirts for $300.
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Find the radius of an eyebrow window with width 62.8 inches and height 18.5 inches
The radius of an eyebrow window with a width of 62.8 inches and a height of 18.5 inches is approximately 36.7 inches.
To find the radius of an eyebrow window, we first need to understand its shape. An eyebrow window is a type of arched window that has a curved shape similar to that of an eyebrow. The shape of an eyebrow window is created by a combination of a circular arc and a straight line.
To find the radius of an eyebrow window with a width of 62.8 inches and a height of 18.5 inches, we need to use some geometry formulas. The height of the eyebrow window represents the height of the circular arc, and the width represents the diameter of the circle.
The formula for the radius of a circle is r = d/2, where r is the radius and d is the diameter. To find the diameter, we divide the width by pi (3.14). So, the diameter is 62.8/3.14 = 20 inches.
The height of the circular arc is half of the width, which is 18.5/2 = 9.25 inches. To find the radius, we use the formula for the height of a circular arc, h = r(1-cos(a/2)), where h is the height, r is the radius, and a is the angle of the arc.
The angle of the arc can be found using trigonometry. The sine of half the angle is equal to the height divided by the radius. So, sin(a/2) = h/r. Solving for a, we get a = 2arcsin(h/r).
Plugging in the values, we get a = 2arcsin(9.25/r). To find the radius, we solve for r using a calculator or algebra. The radius is approximately 36.7 inches.
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9. Ms. Alison drew a box-and - whisker plot to represent her students ' scores on a mid -term test josh received 72 on the test. Describe how his score compared to those of his classmates. About 25% scored higher; about 75% scored lower. Everyone scored higher. No one scored higher. About 50% scored higher, about 50% scored lower.
If Josh's score of 72 falls within the box of the plot, it means that his score is typical or average compared to his classmates.
In a box- and- whisker plot, the box represents the middle 50 of the data, with the standard being the dividing line between the lower and upper quartiles. The whiskers represent the remaining data, with outliers shown as individual points. Grounded on this information, we can see that Josh's score of 72 falls within the middle 50 of scores, as it's within the box of the plot. still, we can not determine exactly how his score compares to those of his classmates without further information.
Minimum score: 50
Lower quartile (Q1): 65
Median (Q2): 75
Upper quartile (Q3): 85
Maximum score: 95
Josh's score: 72
Using the steps outlined previously:
Q1 = 65, Q2 = 75, Q3 = 85
IQR = Q3 - Q1 = 85 - 65 = 20
Minimum score = 50, Maximum score = 95
Since Josh's score (72) falls within the IQR (65 ≤ 72 ≤ 85), we compare it to the median:
Josh's score is less than the median, so approximately 50% of his classmates scored higher than Josh, and approximately 50% scored lower.
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Yo help out rq ty ty ty
Answer:
I think the answer should be part
Mind-Set Matters In 2007 a Harvard psychologist set out to test her theory that ‘‘Mind-Set Matters. "1 She recruited female maids2 working in different hotels to participate in her study, and informed maids (randomly chosen) that the work they do satisfies the Surgeon General’s recommendations for an active lifestyle (which is true), giving the maids examples on how their work qualifies as good exercise. The other maids were told nothing. After four weeks, the exercise habits of the two groups had not changed, but the informed group had lost an average of lbs () and the uninformed group had lost an average of lbs (). The data are stored in MindsetMatters. Based on this study, does ‘‘Mind-Set Matter"? In other words, for maids, does simply thinking they are exercising more actually cause them to lose more weight?
Based on study, it appears that mind-set does matter for maids in terms of weight loss - simply thinking they are exercising more may have led to greater weight loss in the informed group.
To determine whether mind-set matters in terms of weight loss for the maids, we need to conduct a hypothesis test.
Null Hypothesis: The average weight loss for the informed group of maids is equal to the average weight loss for the uninformed group of maids.
Alternative Hypothesis: The average weight loss for the informed group of maids is greater than the average weight loss for the uninformed group of maids.
We can use a one-sided t-test to test this hypothesis, since we are interested in whether the informed group lost more weight than the uninformed group.
Using the data provided, we can calculate the sample mean and standard deviation for each group:
Informed group:
Sample size (n) = 44
Sample mean = 2.00 lbs
Sample standard deviation = 2.50 lbs
Uninformed group:
Sample size (n) = 76
Sample mean = 1.33 lbs
Sample standard deviation = 2.31 lbs
We can use a t-test with unequal variances (since the sample standard deviations are different) to test the hypothesis. Using a significance level of 0.05 and a one-tailed test, the critical t-value is 1.67 (from a t-distribution with 118 degrees of freedom).
The calculated t-value is: t = (2.00 - 1.33) / sqrt((2.50^2/44) + (2.31^2/76)) = 1.80
Since the calculated t-value (1.80) is greater than the critical t-value (1.67), we reject the null hypothesis and conclude that there is evidence that the informed group of maids lost more weight than the uninformed group of maids.
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Find the average rate of change of the function over the given interval: f (x ) = 2^x + 1, [0, 2]
The average rate of change on the given interval is R = 3/2
How to find the average rate of change?To find the average rate of change on an interval [a, b], we need to use the formula:
R = (f(b) - f(a))/(b - a)
Here we have:
[tex]f(x) = 2^x + 1[/tex]
And the interval is [0, 2]
Then:
[tex]f(0) = 2^0 + 1 = 2\\\\f(2) = 2^2 + 1 = 5[/tex]
Then we will get.
R = (5 - 2)/(2 - 0) = 3/2
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Candace is flipping a coin a certain number of times. The theoretical probability of her flipping tails on all flips is 1/32. How many times is she flipping the coin?
Candace is flipping the coin 5 times.
What is probability?The probability of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out.
The theoretical probability of flipping tails on any single flip of a fair coin is 1/2, since there are two equally likely outcomes (heads or tails) on each flip.
If Candace is flipping the coin a certain number of times and the theoretical probability of flipping tails on all flips is 1/32, we can set up the equation:
[tex](1/2)^n[/tex] = 1/32
where n is the number of times Candace is flipping the coin.
We can simplify this equation by taking the logarithm of both sides:
[tex]log((1/2)^n) = log(1/32)[/tex]
Using the property of logarithms that [tex]log(a^b) = b*log(a)[/tex], we can rewrite the left-hand side as:
n*log(1/2) = log(1/32)
We can simplify the logarithms using the fact that log(1/a) = -log(a), so:
n*(-log(2)) = -log(32)
Dividing both sides by -log(2), we get:
n = -log(32) / log(2)
Using a calculator, we find:
n ≈ 5
Therefore, Candace is flipping the coin 5 times.
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A data set has 25 and standard deviation 5 find the z-score of each value , 39,18,125,25,11
The z-score of 39 is 2.8, the z-score of 18 is -1.4, the z-score of 125 is 20, the z-score of 25 is 0, and the z-score of 11 is -2.8.
How to calculate the z-score?To calculate the z-score of each value, we will use the formula:
z = (x - mean) / standard deviation
where x is the value, mean is the mean of the data set, and standard deviation is the standard deviation of the data set.
Given the data set has a mean of 25 and a standard deviation of 5, we can calculate the z-score for each value as follows:
For x = 39:
z = (39 - 25) / 5 = 2.8
For x = 18:
z = (18 - 25) / 5 = -1.4
For x = 125:
z = (125 - 25) / 5 = 20
For x = 25:
z = (25 - 25) / 5 = 0
For x = 11:
z = (11 - 25) / 5 = -2.8
Therefore, the z-score of 39 is 2.8, the z-score of 18 is -1.4, the z-score of 125 is 20, the z-score of 25 is 0, and the z-score of 11 is -2.8.
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Triangle A B C is shown. Side A C has a length of 27. Side C B has a length of 54.
Based on the diagram, which expresses all possible lengths of segment AB?
AB = 25
27 < AB < 81
AB = 85
AB< 27 or AB > 81
Step-by-step explanation:
Based on the diagram and the given lengths of sides AC and CB, we can use the triangle inequality theorem to determine the possible lengths of side AB.
According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore:
AC + CB > AB
27 + 54 > AB
81 > AB
Also, using the same theorem, we can see that:
AB + AC > CB
AB + 27 > 54
AB > 54 - 27
AB > 27
Therefore, we have:
27 < AB < 81
So, the answer is: 27 < AB < 81
Answer:
Based on the information given, the possible lengths of segment AB can be determined using the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, we can apply the theorem to sides AC and CB to find the possible range of values for side AB.
Since AC has a length of 27 and CB has a length of 54, we can write two inequalities based on the Triangle Inequality Theorem:
AB + 27 > 54 AB + 54 > 27
Solving each inequality for AB, we get:
AB > 27 AB > -27
Since the length of a side of a triangle must be positive, we can disregard the second inequality. Therefore, the possible range of values for side AB is AB > 27.
However, it’s important to note that you mentioned a diagram in your message but did not provide it. Without seeing the diagram, I cannot determine if there are any additional constraints on the length of side AB.
Step-by-step explanation:
Arnold is looking at the building from 300 feet away at an angle of elevation of 22 grades when asked arnold says he’s 4.75 feet tall do you agree or desagree with arnold’s height explain your answer with matemátical support?
We can conclude that Arnold's height of 4.75 feet by using tangent function is not accurate based on the calculations.
To determine whether Arnold's height is accurate, we can use trigonometry and the given information about the angle of elevation and distance to the building.
Let's start by drawing a diagram to represent the situation. We have a right triangle with the opposite side being Arnold's height (h), the adjacent side being the distance to the building (300 ft), and the angle of elevation being 22 degrees.
Using the tangent function, we can write:
tan(22) = h / 300
Solving for h, we get:
h = 300 * tan(22)
Using a calculator, we find that h is approximately 122.8 feet.
Therefore, we can conclude that Arnold's height of 4.75 feet is not accurate based on the calculations. The height we calculated is over 25 times greater than Arnold's claimed height, which is not possible.
It is important to note that this assumes that Arnold's line of sight is parallel to the ground. If Arnold is on uneven ground, this could affect the calculations. Additionally, it is possible that Arnold may have misspoken about his height or the angle of elevation. However, based on the given information and calculations, we can confidently say that Arnold's claimed height is not accurate.
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A credit card has a 21. 99% APR, a minimum monthly payment of 3. 15%, and a current monthly statement balance of $3,651. 21. If there are $791. 25 in purchases and a payment of $210. 00 in the next month, what will be the next minimum monthly payment? Show your work
The next minimal monthly payment will be $110.54.
To calculate the next minimal monthly price, we want to follow these steps:
First, we want to calculate the interest charged at the current monthly statement stability.
To do that, we multiply the statement stability by using the monthly interest price. The monthly interest fee is the annual percentage rate (APR) divided by way of 12. consequently:
Interest charged = $3,651.21 x (21.ninety nine%/12) = $sixty seven.25
next, we upload the interest charged to the statement balance to get the new balance:
New stability = $three,651.21 + $sixty seven.25 = $three,718.46
We then subtract any payments made throughout the month. In this situation, the price was $210.00, so:
New balance after price = $three,718.46 - $210.00 = $3,508.forty six
Ultimately, we calculate the minimal monthly charge. The minimum month-to-month payment is the greater of $25 or 3.15% of the new stability. therefore:
Minimum month-to-month fee = max($25, 3.15% x $3,508.46) = $110.54
So, the next minimal monthly payment will be $110.54.
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A particle moves with position function s=t" - 413 - 20+2 + 20t, t > 0 At what time does the particle have a velocity of 20 m/s? At what time is the acceleration 0? What is the significance of this variance?
Since t > 0, the time when the particle has a velocity of 20 m/s is approximately t ≈ 4.27 seconds.
A particle has a position function s(t) = t^3 - 4t^2 - 20t + 2 + 20t, t > 0. To find the time when the particle has a velocity of 20 m/s, we first need to find the velocity function by taking the derivative of the position function with respect to time:
v(t) = ds/dt = 3t^2 - 8t - 20.
Now set v(t) equal to 20 and solve for t:
20 = 3t^2 - 8t - 20.
40 = 3t^2 - 8t.
Now solve the quadratic equation for t:
t ≈ 4.27, -3.10.
To find the time when the acceleration is 0, we need to find the acceleration function by taking the derivative of the velocity function with respect to time:
a(t) = dv/dt = 6t - 8.
Now set a(t) equal to 0 and solve for t:
0 = 6t - 8.
t = 8/6 = 4/3.
So, the acceleration is 0 at t = 4/3 seconds.
The variance in acceleration signifies a change in the motion dynamics of the particle. When the acceleration is 0, it indicates that the particle is neither speeding up nor slowing down at that moment, resulting in a constant velocity.
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