The function f(n) = n - 3 maps distinct integers to distinct integers, and thus is injective.
(a) The function f(n) = n - 3 is one-to-one (injective). To prove this, suppose that f(a) = f(b) for some integers a and b. Then, we have a - 3 = b - 3, which implies a = b. Therefore, the function f(n) = n - 3 maps distinct integers to distinct integers, and thus is injective.
(b) The function f(n) = n^2 - 1 is not one-to-one (not injective). To see this, note that f(1) = f(-1) = 0, so different inputs map to the same output. In general, for any positive integer k, we have f(k) = f(-k), since (k^2 - 1) = ((-k)^2 - 1). Therefore, the function f(n) = n^2 - 1 is not injective.
(c) The function f(n) = n^5 is one-to-one (injective). To prove this, suppose that f(a) = f(b) for some integers a and b. Then, we have a^5 = b^5, which implies a = b (since the fifth root of a non-zero real number is unique). Therefore, the function f(n) = n^5 maps distinct integers to distinct integers, and thus is injective.
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Question 2
State the probability that a randomly selected, normally
distributed value lies between
a) o below the mean and o above the mean (round to
the nearest hundredths)
b) 20 below the mean and 20 above the mean (round
to the nearest hundredths)
The probability of a randomly selected, normally distributed value lying between 20 below the mean and 20 above the mean is 0.9545 (rounded to the nearest hundredth).
What is the fundamental concept of probability?A number between zero and one represents the probability that an occurrence will take place. An event is a predefined set of random variable outcomes. Only one mutually exclusive event can occur at a time. Exhaustive events encompass or include all possible outcomes.
We can calculate the probabilities of a randomly chosen value falling between different z-scores using the provided standard normal distribution table.
a) The probability of a value being 0 below or above the mean is the same as the probability of a value being -1 to 1 standard deviations from the mean. According to the standard normal distribution table, the probability of a z-score between -1 and 1 is 0.6827. As a result, the probability of a randomly chosen, normally distributed value falling between 0 below and 0 above the mean is 0.6827. (rounded to the nearest hundredth).
b) The probability of a value falling between 20 and 20 standard deviations from the mean is the same as the probability of a value falling between -20/10 and 20/10 standard deviations from the mean (since the standard deviation is 10). According to the standard normal distribution table, the probability of a z-score between -2 and 2 is 0.9545. As a result, the probability of a randomly chosen, normally distributed value falling between 20 below and 20 above the mean is 0.9545. (rounded to the nearest hundredth).
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A fair coin is tossed five times. What is the theoretical probability that the coin lands on the same side every time??
A) 0.1
B) 0.5
C) 0.03125
D) 0.0625
Answer:
The answer is C
Step-by-step explanation:
Assuming this is a fair coin, the theoretical probability of the coin going on one side, let's say heads, is 50%, or 0.5. So what's the chance the coin lands head 5 times? To do this we do 0.5^5 OR 0.5*0.5*0.5*0.5*0.5. Both of these answers equal 0.03125. So C is the Answer. Hope this helps :D
lighting, inc. uses direct labor hours as a basis for allocating overhead. next year's estimated total overhead is $180000 and direct labor hours are predicted to be $30000 hours. the average labor cost is $10 per. what is the predetermined overhead rate
Answer:
The predetermined overhead rate is calculated as follows:
Predetermined overhead rate = Estimated total overhead / Estimated total direct labor hours
In this case, the estimated total overhead is $180,000, and the estimated total direct labor hours are 30,000. Therefore:
Predetermined overhead rate = $180,000 / 30,000 hours
Predetermined overhead rate = $6 per direct labor hour
So, the predetermined overhead rate is $6 per direct labor hour.
Baker School's hockey games are 60 minutes long. Nico played for 30 minutes of the last game. What percent of the game time did Nico play?
Pick the model that represents the problem.
Dude he played for 1/2 of the game half of 60 is 30.
50%.
I'm I missing something?
Ciara throws four fair six-sided dice. The faces of each dice are labelled with the numbers 1, 2, 3, 4, 5, 6 Work out the probability that at least one of the dice lands on an even number.
The likelihood that one or more of the dice will land on an even number is 1296.
How does probability work?The likelihood of an event is quantified by its probability, which is a number. It is stated as a number between 0 and 1, or in percentage form, as a range between 0% and 100%. The likelihood of an event increasing with probability of occurrence.
According to the given information:Four 6-sided dice are rolled what is the probability that at least two dice show least 2 die the same.
For 2 of the same: 5×5×642) =900
For 3 of the same: 5×643) =120
For 4 of the same: 644) =6
Combined: 900+120+6=1026
Total possibilities: 64=1296
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The probability that at least one of the dice lands on an even number is 15/16 or approximately 0.938.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
We can solve this problem by finding the probability that all four dice land on odd numbers and then subtracting this probability from 1 to get the probability that at least one of the dice lands on an even number.
The probability that one dice lands on an odd number is 3/6 = 1/2, and the probability that all four dice land on odd numbers is:
(1/2) × (1/2) × (1/2) × (1/2) = 1/16
Therefore, the probability that at least one of the dice lands on an even number is:
1 - 1/16 = 15/16
So the probability that at least one of the dice lands on an even number is 15/16 or approximately 0.938.
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Find the average rate of change of the area of a circle withrespect to its radius r as r changes from2 to each of the following.(i) 2 to 3 (ii) 2 to 2.5 (iii) 2 to 2.1
The average rate of change is 5π; for r changing from 2 to 2.5, it is 2.5π, and for r changing from 2 to 2.1, it is 4.1π.
The area of a circle is given by the formula A = πr². To find the average rate of change of A with respect to r, we can take the derivative of A with respect to r:
dA/dr = 2πr
This tells us how much the area changes for a small change in the radius. To find the average rate of change over a larger interval, we can use the formula:
ΔA/Δr = (A2 - A1)/(r2 - r1)
where A1 and A2 are the areas at the initial and final radii, and r1 and r2 are the initial and final radii.
(i) For r changing from 2 to 3:
ΔA/Δr = (π(3)² - π(2)²)/(3 - 2) = 5π
The average rate of change of the area with respect to the radius is 5π.
(ii) For r changing from 2 to 2.5:
ΔA/Δr = (π(2.5)² - π(2)²/(2.5 - 2) = 2.5π
The average rate of change of the area with respect to the radius is 2.5π.
(iii) For r changing from 2 to 2.1:
ΔA/Δr = (π(2.1)² - π(2)²)/(2.1 - 2) = 4.1π
The average rate of change of the area with respect to the radius is 4.1π.
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A triangular prism has height 20 cm.
Its triangular face has base 7 cm and height 10 cm.
A. what is the volume of the prism?
B. suppose you triple the height of the prism.what happen to the volume?
C. suppose you triple the base of the triangular face.what happen to the volume?
D. suppose you triple the height of the triangular face.what happen to the volume?
E. suppose you triple all 3 dimensions.what happen to the volume?
Answer:
A. The volume of the triangular prism can be calculated using the formula V = (1/2)bh × h, where b is the base of the triangular face and h is the height of the prism. Thus, V = (1/2)(7 cm)(10 cm) × 20 cm = 700 cubic centimeters.
B. If the height of the prism is tripled to 60 cm, then the new volume would be V' = (1/2)(7 cm)(10 cm) × 60 cm = 2100 cubic centimeters. Thus, the volume is tripled.
C. If the base of the triangular face is tripled to 21 cm, then the new volume would be V' = (1/2)(21 cm)(10 cm) × 20 cm = 2100 cubic centimeters. Thus, the volume is tripled.
D. If the height of the triangular face is tripled to 30 cm, then the new volume would be V' = (1/2)(7 cm)(30 cm) × 20 cm = 2100 cubic centimeters. Thus, the volume is tripled.
E. If all three dimensions (base, height of triangular face, and height of prism) are tripled, then the new volume would be V' = (1/2)(21 cm)(30 cm) × 60 cm = 18900 cubic centimeters. Thus, the volume is multiplied by a factor of 27.
12. Reason A data set is represented by the box plot shown. Between which two values would the middle 50% of the data be found? Explain.
The middle 50% data of the boxplot will be calculated between the value of 7 to 14.
Explain about the box plot?The variation in information is shown using a boxplot, which is a standardized method based on a five-number summary ("minimum," first quartile ("Q1"), median ("Q3"), and "maximum"). It can reveal information about your outliers' values. Boxplots can also show you exactly securely your data is grouped, whether or not your data is skewed, and whether or not your data is symmetrical.The data set ranges are:
4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17
Divide the given data in 4 quartiles Qs;
Q1 = 4 - 6
Q2 = 7 - 10
Q3 = 11 - 14
Q4 = 15 - 17
Thus, 50% data will be lying in Q2 and Q3.
Range - 7 - 14
Thus, the middle 50% data of the box plot will be calculated between the value of 7 to 14.
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ab and bc are perpendicular lines find the value of x of 25
Answer:
If the time is 3:45 how many minutes is it slow or fast
Elizabeth works as a server in coffee shop, where she can earn a tip (extra money) from each customer she serves. The histogram below shows the distribution of her 60 tip amounts for one day of work. 25 g 20 15 10 6 0 0 l0 15 20 Tip Amounts (dollars a. Write a few sentences to describe the distribution of tip amounts for the day shown. b. One of the tip amounts was S8. If the S8 tip had been S18, what effect would the increase have had on the following statistics? Justify your answers. i. The mean: ii. The median:
a. Histogram shows tip amounts ranging between $6 and $25, skewed to the right with a longer tail of higher tips.
b. Increasing the $8 tip to $18 would increase the mean since total tip amount increases by $10 spread out over 60 customers. Median won't be affected since changing one value does not alter the middle value.
a. The histogram shows that Elizabeth received a range of tip amounts, with the majority of tips falling between $6 and $25. The distribution is skewed to the right, with a longer tail of higher tip amounts.
b. i. The mean would increase because the total tip amount would increase by $10, and this increase would be spread out over the 60 customers.
ii. The median would not be affected because it is the middle value when the data is ordered, and changing one value does not change the middle value.
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For the functions f(x)=−7x+3 and g(x)=3x2−4x−1, find (f⋅g)(x) and (f⋅g)(1).
Answer: (f⋅g)(1) = 10.
Step-by-step explanation:
To find (f⋅g)(x), we need to multiply the two functions f(x) and g(x) together. This can be done by multiplying each term of f(x) by each term of g(x), and then combining like terms. We get:
(f⋅g)(x) = f(x) * g(x)
= (-7x+3) * (3x^2 - 4x - 1)
= -21x^3 + 28x^2 + x - 3x^2 + 4x + 1
= -21x^3 + 25x^2 + 5x + 1
To find (f⋅g)(1), we can substitute x=1 into the expression for (f⋅g)(x):
(f⋅g)(1) = -21(1)^3 + 25(1)^2 + 5(1) + 1
= -21 + 25 + 5 + 1
= 10
Therefore, (f⋅g)(1) = 10.
which of the following numeric measures would be most likely to produce invalid statistical analysis?
The most likely to produce invalid statistical analysis of numeric measures is Pain rating as: none = 0; slight = 1; much = 2, as it is an ordinal scale of measurement, which does not have equal intervals between the categories. So, the correct answer is B).
It means that the differences between the categories are not necessarily equivalent, and therefore, any statistical analysis based on this scale may not accurately reflect the true relationship between variables.
The other options (blood pressure in mmHg, oxygen saturation in percentage, neonatal birth weight in kilograms) are measured on interval or ratio scales, which have equal intervals between values and can be used for meaningful statistical analysis. so, the correct option is B).
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____The given question is incomplete, the complete question is given below:
Which of the following numeric measures would be most likely to produce invalid statistical analysis?A)Analysis of patients' blood pressures in mmHgB)Pain rating as: none = 0; slight = 1; much = 2C)Assessment of oxygen saturation in percentageD)Analysis of neonatal birthweight in kilogr
a. Use the summary to determine the point estimate of the population mean and margin of error for the confidence interval
b. interpret the confidence interval
c. verify the results by computing a 95% confidence interval with the information provided
d. why is the margin of error for this confidence interval so small?A study asked respondents, "If ever married, how old were you when you first married? The results are summarized in the technology excerpt that follows. Complete parts (a) through (d) below. One-Sample T: AGEWED Variable N Mean StDev SE Mean 99.0% CI AGEWED 26920 21.890 4.787 0.029 (21.815, 21.965) L attention and maintarhaan Hansen
The point estimate for the population mean age at first marriage is 21.89, the true population mean age at first marriage falls between 21.815 and 21.965 years with a small margin of error due to a large sample size. A 99% confidence interval is (21.836, 21.944).
The point estimate at first marriage is 21.89.
We can interpret the 99% confidence interval as follows: we are 99% confident that the true population mean age at first marriage falls between 21.815 and 21.965 years.
To compute a 95% confidence interval, we can use the formula:
Margin of error = z*(SE)
where z is the z-score corresponding to the desired confidence level (1.96 for 95% confidence), and SE is the standard error of the mean, which is equal to the standard deviation divided by the square root of the sample size.
Thus, for the given data:
Margin of error = 1.96*(4.787/sqrt(26920)) = 0.054
The 95% confidence interval can be computed as:
21.89 ± 0.054
which gives us a range of (21.836, 21.944).
The margin of error for this confidence interval is small because the sample size is very large (n=26920). As the sample size increases, the standard error of the mean decreases, which in turn reduces the margin of error.
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_____The given question is incomplete, the complete qustion is given below:
a. Use the summary to determine the point estimate of the population mean and margin of error for the confidence interval
b. interpret the confidence interval
c. verify the results by computing a 95% confidence interval with the information provided
d. why is the margin of error for this confidence interval so small? A study asked respondents, "If ever married, how old were you when you first married? The results are summarized in the technology excerpt that follows. Complete parts (a) through (d) below. One-Sample T: AGEWED Variable N Mean StDev SE Mean 99.0% CI AGEWED 26920 21.890 4.787 0.029 (21.815, 21.965) L attention and maintarhaan Hansen
0.0125 inches thick
Question 4
1 pts
The combined weight of a spool and the wire it carries is 13.6 lb. If the weight of the spool is 1.75 lb.,
what is the weight of the wire?
Question 5
1 pts
In linear equation, 11.85 pounds is the weight of the wire.
What is linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.
Total weight of pool having 16 wires =13.6 pounds
Weight of the pool =1.75
Therefore the weight of the wire alone = 13.6 - 1.75
= 11.85 pounds
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If the area of one side of this cube is 25 cm^2
2
, what is the area of the whole surface of the cube?
cm^2
2
Answer:
150 cm2
Step-by-step explanation:
Given side of cube's area = 25. Since Side's a square,
Edge^2 = 5^2 = 5 cm
Total surface area: 6*a² = 6*5*5 = 150 cm2
under the normal distribution, if the mean of the distribution of raw scores is equal to 100, then its equivalent z-score is equal to
The equivalent z-score for a raw score of 115 under a normal distribution with a mean of 100 and a standard deviation of 15 is 1.
Under the normal distribution, if the mean of the distribution of raw scores is equal to 100 and the standard deviation is known, we can use the z-score formula to calculate the equivalent z-score for any given raw score.
The z-score formula is given by:
z = (x - μ) / σ
where x is the raw score, μ is the mean of the distribution, σ is the standard deviation of the distribution, and z is the corresponding z-score.
Since the mean of the distribution is 100, we have μ = 100. To calculate the z-score, we need to know the standard deviation of the distribution or have information about the distance of the raw score from the mean in terms of standard deviations.
If we assume that the standard deviation is 15, which is a common value used in educational testing, and the raw score is 115, then the corresponding z-score would be:
z = (115 - 100) / 15 = 1
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The weight of a small Starbucks coffee is a normally distributed random variable with a mean of 360 grams and a standard deviation of 9 grams Find the weight that corresponds to each event(use excel or appendix c to calculate the z value round your final answers to the 2 decimal places)
URGENT
The weight that corresponds to this event are approximately 344.03 grams and 375.97 grams.
How to deal with normally distribution?To find the weight that corresponds to each event, we need to use the standard normal distribution, which has a mean of 0 and a standard deviation of 1. We can convert the given mean and standard deviation to z-scores using the formula:
z = (x - μ) / σ
where x is the weight we want to find, μ is the mean (360 grams), and σ is the standard deviation (9 grams).
Then, we can use a standard normal distribution table or calculator to find the probability of each event, and convert it back to a weight using the inverse of the z-score formula:
x = μ + z * σ
where z is the z-score that corresponds to the desired probability.
Event 1: The weight is less than 345 grams.
z = (345 - 360) / 9 = -1.67
Using a standard normal distribution table or calculator, we find that the probability of a z-score less than -1.67 is approximately 0.0475.
x = 360 + (-1.67) * 9 = 344.03 grams
Therefore, the weight that corresponds to this event is approximately 344.03 grams.
Event 2: The weight is between 355 and 365 grams.
First, we need to find the z-scores that correspond to the two boundaries:
z1 = (355 - 360) / 9 = -0.56
z2 = (365 - 360) / 9 = 0.56
Using a standard normal distribution table or calculator, we find that the probability of a z-score less than -0.56 is approximately 0.2123, and the probability of a z-score less than 0.56 is approximately 0.7123. Therefore, the probability of a z-score between -0.56 and 0.56 is:
0.7123 - 0.2123 = 0.5
x1 = 360 + (-0.56) * 9 = 355.16 grams
x2 = 360 + (0.56) * 9 = 364.84 grams
Therefore, the weight that corresponds to this event is any weight between 355.16 and 364.84 grams.
Event 3: The weight is greater than 375 grams.
z = (375 - 360) / 9 = 1.67
Using a standard normal distribution table or calculator, we find that the probability of a z-score greater than 1.67 is approximately 0.0475.
x = 360 + (1.67) * 9 = 375.97 grams
Therefore, the weight that corresponds to this event is approximately 375.97 grams.
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xercise 1.3.4 in each case, either express y as a linear combination of a1, a2, and a3, or show that it is not such a linear combination. here:
Here, y can be expressed as a linear combination of a1, a2, and a3 is y = (-1/8) a1 + (9/4) a2 - (5/2) a3.
We can express y as a linear combination of a1, a2, and a3 if and only if y is a linear combination of the column vectors of the matrix A whose columns are a1, a2, and a3. We can write this as:
y = c1 a1 + c2 a2 + c3 a3
where c1, c2, and c3 are constants to be determined. We can solve for these constants by writing the system of equations in matrix form:
A [c1; c2; c3] = y
where [c1; c2; c3] is a column vector of the constants c1, c2, and c3. We can solve for [c1; c2; c3] by multiplying both sides by the inverse of A (assuming it exists):
[c1; c2; c3] = A^(-1) y
If A^(-1) exists, then y can be expressed as a linear combination of a1, a2, and a3. Otherwise, y cannot be expressed as a linear combination of a1, a2, and a3.
For y = [1 2 4 0], we have:
A = [-1 3 0 1; 3 1 2 0; 1 1 1 1]
We can compute the inverse of A using row reduction:
[A | I] = [-1 3 0 1 | 1 0 0;
3 1 2 0 | 0 1 0;
1 1 1 1 | 0 0 1]
[R2 - 3R1, R3 - R1] = [-1 3 0 1 | 1 0 0;
0 -8 2 -3 | -3 1 0;
0 -2 1 0 | -1 0 1]
[R2 / (-8), R3 + 2R2] = [1/8 -3/8 0 3/8 | 3/8 -1/8 0;
0 1 0 -1/4 | 3/4 -1/4 0;
0 0 1 -1/2 | 1/2 -1/2 1]
Therefore, A^(-1) = [1/8 -3/8 0 3/8;
0 1 0 -1/4;
0 0 1 -1/2;
0 0 0 0]
We can now compute [c1; c2; c3]:
[c1; c2; c3] = A^(-1) y = [1/8 -3/8 0 3/8;
0 1 0 -1/4;
0 0 1 -1/2;
0 0 0 0] [1; 2; 4; 0] = [-1/8; 9/4; -5/2; 0]
Therefore, y as a linear combination of a1, a2, and a3:
y = (-1/8) a1 + (9/4) a2 - (5/2) a3
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_____The given question is incomplete, the complete question is given below:
Exercise 1.3.4 in each case, either express y as a linear combination of a1 = [-1 3 0 1], a2 = [3 1 2 0], and a3= [1 1 1 1], or show that it is not such a linear combination. here: y = [1 2 4 0]
a rectangular prism with a volume of 20 in^3 is dialited with a scale facotr of 2. what is the volume of the new figure?
The volume of the new rectangular prism is 160 in³ after it has been dilated with a scale factor of 2.
In this case, the scale factor is 2, which means that the dimensions of the original figure will be multiplied by 2 to get the dimensions of the new figure.
Volume of rectangular prism = length x width x height
20 = l x w x h
Next, we need to find the new dimensions of the rectangular prism after it has been dilated by a scale factor of 2. We can do this by multiplying each dimension of the original rectangular prism by 2.
New length = 2 x l
New width = 2 x w
New height = 2 x h
Now we can find the volume of the new rectangular prism by using the same formula as before, but with the new dimensions:
Volume of new rectangular prism = (2 x l) x (2 x w) x (2 x h)
Simplifying this expression, we get:
Volume of new rectangular prism = 8 x (l x w x h)
We know that l x w x h is equal to the volume of the original rectangular prism, which is 20 in³. So we can substitute this value into the expression to get:
Volume of new rectangular prism = 8 x 20 in³
Volume of new rectangular prism = 160 in³
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find the equation of the line with slope 2 that goes through the point (6,1). answer using slope-intercept form.
The equation of the line with slope 2 that goes through the point (6,1) in slope-intercept form is y = 2x - 11. This means that the y-intercept of the line is -11, and the slope of the line is 2, which means that for every increase of 1 in x, the line will increase by 2 in y.
To find the equation of a line with a given slope and a point on the line, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is the given point on the line.
In this case, the slope is given as 2 and the point (6,1) is on the line. Plugging these values into the equation, we get:
y - 1 = 2(x - 6)
Expanding the right side, we get:
y - 1 = 2x - 12
Adding 1 to both sides, we get:
y = 2x - 11
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Solve the following problems.
Given: AABC, DE AC,
BD DC, mZ1=m22,
mZBDC= 100°
Find: m< A, m< b , m
The value of the angles in the triangle are:
∠A = 60°, ∠B = 80° and ∠C = 40°
How to find the value of m∠A, m∠B, m∠C in the triangle?
We are given that BD = DC
Thus, ∠DBC = ∠BCD ---- 1 (angle in isosceles triangle)
We also have ∠BDC = 100°
In ΔBDC
∠BDC + ∠DBC + ∠BCD = 180° (sum of angles of triangle is 180°)
Using 1:
∠BDC + 2∠DBC = 180°
100° + 2∠DBC = 180°
2∠DBC = 180 - 100
2∠DBC = 80
∠DBC = 80/2
∠DBC = 40°
∠DBC = ∠BCD = ∠2 = 40°
Thus, ∠C = 40°
We are given that m∠1 = m∠2
Thus, ∠1 = ∠2 = 40°
Now, ∠BDC + ∠BDA = 180° (Linear pair)
100° + ∠BDA = 180°
∠BDA = 180 - 100
∠BDA = 80°
In ΔABD
∠ABD + ∠BDA + ∠BAD = 180° (sum of angles of triangle is 180°)
∠1 + ∠BDA + ∠BAD = 180°
40° + 80° + ∠BAD = 180°
120° + ∠BAD = 180°
∠BAD = 60°
So, ∠A = 60°
∠B = ∠1 + ∠2 = 40° + 40° = 80°
Therefore, ∠A = 60°, ∠B = 80° and ∠C = 40°
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Complete Question
m∠1=m∠2
D∈
AC
, BD = DC
m∠BDC = 100°
Find: m∠A, m∠B, m∠C
I will mark you brainiest!
What is the length of BC?
A) 1.7
B) 2.1
C) 3.8
D) 4.6
Answer:
B. 2.1
Step-by-step explanation:
If you draw a line from C to intersect AB perpendicularly at point D so we have 2 right triangles ACD and BCD.
For △ACD, AC is hypotenuse so sinA = CD/AC
=> CD = 5 x sin(20) = 5 x 0.342 = 1.71
then we have AB = AD + BD
Pythagorean theorem: c^2 = a^2 + b^2
for △ACD, 5^2 = 1.71^2 + AD^2
AD^2 = 5^2 - 1.71^2 = 22.0759
AD = 4.70
BD = AB - AD = 6 - 4.70 = 1.30
for △BCD, BC is hypotenuse
BC^2 = BD^2 + CD^2 = 1.30^2 + 1.71^2 = 4.61
BC = √4.61 = 2.1
Given that x is a positive integer less than 100, how many solutions does the congruence x+13=55 (mod 34) have?
The congruence x + 13 ≡ 55 (mod 34) simplifies to x ≡ 12 (mod 34). There are three solutions for x less than 100 that satisfy this congruence.
The given congruence is x + 13 ≡ 55 (mod 34). Simplifying this, we get x ≡ 12 (mod 34).
We need to find the number of solutions for x that are less than 100 and satisfy this congruence.
The general solution for the congruence x ≡ 12 (mod 34) is x = 12 + 34k, where k is an integer.
The solutions that are less than 100 are obtained when k = 0, 1, or 2.
Thus, the number of solutions is 3.
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-0.1x^2+10=0
find the x
Answer:
x = ±10
Step-by-step explanation:
1) Subtract 10 from both sides.
[tex]-0.1 \times x^2=-10[/tex]
2) Divide both sides by -0.1.
[tex]x^2=\frac{-10}{-0.1}[/tex]
3) Simplify [tex]\frac{-10}{-0.1}[/tex] to 100.
[tex]x^2=100[/tex]
4) Take the square root of both sides.
[tex]x=\pm \sqrt{100}[/tex]
5) Since 10 * 10 is 100, the square root of 100 is 10.
[tex]x=\pm10[/tex]
What is the amount of interest to be paid if u got a reducing balance loan of $2700 and you will repay it over 5 years by quarterly installments of $1899.75 at interest rate 14% p.a. (compounded quarterly)
The total interest to be paid over the 5-year period is $403.22.
What is reducing balance loan?In a loan with a declining balance, interest is added to the outstanding balance at the start of each period, such as each month or each quarter. The outstanding balance, which decreases as the borrower makes repayments, is used to determine the interest rate. As a result, the borrower gradually pays less interest and more of each payment is used to lowering the main balance due. The lowering balance approach is frequently applied to mortgages, personal loans, and auto loans.
Given that, the quarterly installments are $1899.75.
For the entire year for a total of 5 years the total amount is:
Total amount = 4 * 5 * $1899.75 = $37995
For reducing balance loan the interest is calculated as:
For the first quarter, the interest to be paid is:
interest = (total amount - 0) * (0.14 / 4)
interest = (37995 - 0) * (0.14 / 4) = $94.50
Similarly for the remaining quarters we have:
Second quarter = $87.95
Third quarter: $81.05
Fourth quarter: $73.76
Fifth quarter: $65.96
The total interest to be paid over the 5-year period is:
$94.50 + $87.95 + $81.05 + $73.76 + $65.96 = $403.22
Hence, the total interest to be paid over the 5-year period is $403.22.
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You earned $1600 in a summer job and you were paid with a check. You are going to open a checking account at Hometown Bank and put $800 into the account. What amount would you fill in for each letter? Please include the letter and then the amount. If there isn't an amount you can write, for example, A) 0 or A) none
The amount in each letter for checking account is Bills - A = 0, Coin B = 0, Checks C = $800, Total D = $1600, Less cash E = $800, and Net deposit F = $800.
What is checking account?A checking account is a type of bank account that enables regular deposits and withdrawals of money by account holders. Checking accounts frequently come with amenities like check writing, debit cards, and internet banking, making them practical for daily usage. Checking accounts typically do not pay interest on the account balance, in contrast to savings accounts. Yet, many checking accounts don't have to maintain a minimum balance and permit unrestricted withdrawals, which makes them perfect for daily transactions.
Given that, you earn $1600, and put $800 in a checking's account thus,
Bills - A = 0
Coin B = 0
Checks C = $800
Total D = $1600
Less cash E = $800
Net deposit F = D - $800 = $1600 - $800 = $800.
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Jamie is going to run for
1
2
2
1
start fraction, 1, divided by, 2, end fraction of an hour at a constant rate, and they want to plan what that rate will be.
1. Write an equation that represents the distance Jamie will run in kilometers (
�
dd) at a rate of
�
rr kilometers per hour.
The distance Jamie will run is equal to half of the rate in kilometers per hour, the equation is d = r (1/2)
What is speed and velocity?Speed is a scalar number that represents the rate of movement of an item. It is described as the distance covered in a certain amount of time, regardless of direction. In contrast, velocity is a vector quantity that accounts for both speed and direction. It is characterised as the pace at which an item shifts in a certain direction. In physics, the idea of velocity is crucial since it aids in explaining how an object's location varies over time and is used to compute other crucial variables like acceleration and momentum.
The distance is calculated using the given formula:
Distance = rate (time)
Given that, the time is 1/2 hour thus:
d = r (1/2)
Thus, the distance Jamie will run is equal to half of the rate in kilometers per hour, and the equation is d = r (1/2).
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The linear sf of two similar shapes is 2:5 if the area of the similar shapes is 78cm determine the area of the bigger solid
The area of the bigger solid is 67.24 cm².
How to calculate the area of solid ?Assume the smaller shape has a length of 2x and a width of 2y. The larger shape would then have 5x length and 5y width.
Because the area of a rectangle is the product of its length and width, the area of the smaller shape is:
Area of smaller shape = 2x * 2y = 4xy
We know that the similar shapes have an area of 78 cm2. As a result, we can write:
4xy + larger area = 78
(larger shape area) / (smaller shape area) = (linear scale factor)²
Substituting the values from the problem yields:
(larger shape area) / (4xy) = (5/2)2 = 25/4
When we multiply both sides by 4xy, we get:
larger shape area = (25/4) * 4xy = 25xy
Now we can plug the expression we discovered for the area of the smaller shape into the equation we found earlier:
4xy + 25xy = 78
29xy = 78
xy = 78/29
Substituting this xy value into the expression we discovered for the area of the larger shape yields:
larger shape area = 25xy = 25 * (78/29) = 67.24 cm2 (rounded to two decimal places)
As a result, the larger shape has an area of approximately 67.24 cm2.
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A spherical balloon is inflated with gas at a rate of 900 cubic centimeters per minute. (a) Find the rates of change of the radius when r-70 centimeters and r 95 centimeters. r 70 X cm/min r = 95 X cm/min
When the radius of spherical balloon r = 70 cm, the rate of change of the radius is approximately 0.002 cm/min and when the radius is 95 cm then the rate of change of the radius is approximately 0.001 cm/min.
The volume of a sphere is given by V = (4/3)πr^3, where r is the radius. Differentiating both sides with respect to time t, we get:
dV/dt = 4πr^2(dr/dt)
where dV/dt is the rate of change of the volume and dr/dt is the rate of change of the radius.
We are given that dV/dt = 900 cm^3/min.
When r = 70 cm, we can solve for dr/dt as follows:
900 = 4π(70)^2(dr/dt)
dr/dt = 900 / (4π(70)^2) ≈ 0.002 cm/min
Therefore, when r = 70 cm, the rate of change of the radius is approximately 0.002 cm/min.
Similarly, when r = 95 cm, we can solve for dr/dt as follows:
900 = 4π(95)^2(dr/dt)
dr/dt = 900 / (4π(95)^2) ≈ 0.001 cm/min
Therefore, when r = 95 cm, the rate of change of the radius is approximately 0.001 cm/min.
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Hmm, try solving 13 to the power of 16 do it the long way :0
and just in case you do
2(2 + ab) + b(r + 3)
The answer of the given question based on solving 13 to the power of 16 is 13 to the power of 16 is 3,947,868,257,259,789. and the simplified expression is 7 + 2ab + br.
What is Expression?A expression is a combination of symbols or values that represents a particular concept or computation.
In mathematics, an expression is a combination of numbers, variables, operators, and/or functions that can be evaluated to produce a numerical result.
an expression is a way to represent an idea, computation, or meaning using a set of symbols or words.
To solve 13 to the power of 16, we can start by multiplying 13 by itself 16 times:
13 × 13 = 169
169 × 13 = 2197
2197 × 13 = 28,561
28,561 × 13 = 371,293
371,293 × 13 = 4,826,389
4,826,389 × 13 = 62,748,857
62,748,857 × 13 = 815,730,721
815,730,721 × 13 = 10,604,807,473
10,604,807,473 × 13 = 137,858,491,849
137,858,491,849 × 13 = 1,792,160,390,737
1,792,160,390,737 × 13 = 23,303,986,079,681
23,303,986,079,681 × 13 = 303,305,489,096,753
303,305,489,096,753 × 13 = 3,947,868,257,259,789
Therefore, 13 to the power of 16 is 3,947,868,257,259,789.
As for the second expression, we can simplify it using the distributive property of multiplication:
2(2 + ab) + b(r + 3) = 4 + 2ab + br + 3b
Simplifying further, we can combine the constant terms:
2(2 + ab) + b(r + 3) = 7 + 2ab + br
So the simplified expression is 7 + 2ab + br.
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