Answer:
$11.22
Step-by-step explanation:
20% of 56.09 = 1/5 of 56.09
Now, we divide 56.09 by 5 to get our answer which when rounded becomes 11.22.
Answer:
$11.22
Step-by-step explanation:
20% = 0.2
We Take
56.09 x 0.2 = $11.218
Round $11.218 will be $11.22
So, the tip amount is $11.22
PLEASE HELP I'LL GIVE THE BRAINLEST
Select the correct answer from each drop-down menu. The scatter plot shows the amount of water in a tank as measured every few minutes. The initial amount of water in tank was 0, 20, 100, or 120 gallons. The line of best fit shows that about 4/3, 3/4, 2/3, or 1/2 gallon(s) of water were lost per minute. The tank will be empty in about 0, 60, 80, or 90 minutes.
Given that the graph is falling downward, it can be seen that the graph is negative.
Before the tank's water level starts to drop, there are 120 gallons there.
Finding the slope of the graph will give us the amount of water that was lost every minute.
Slope is equal to a climb or a run.
increase = water in gallons
run equals time in minutes.
Slope equals y2 - y1 / x2 - x1
Two points will be chosen from the graph.
( 30, 80) and (60, 40) (60, 40)
Let x1=30, y1=80, x2=60, and y2=40.
Slope = 40 - 80 / 60 - 30
Slope = -40 / 30
Slope = -4/3
The result in the negative represents a loss in gallons of water per minute.
According to the line of best fit, a gallon of water was lost every minute or so.
The graph indicates that the tank will be empty in around 60 minutes.
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when performing a hypothesis test based on a 95% confidence level, what are the chances of making a type ii error?
When performing a hypothesis test based on a 95% confidence level, the chances of making a type II error are 5%.
The process of hypothesis testing is used to determine whether or not a given statistical hypothesis is valid. The objective of this method is to determine whether the null hypothesis can be accepted or rejected based on the sample data obtained.
Hypothesis testing can be used to evaluate two hypotheses. The null hypothesis is the one that must be accepted or rejected, while the alternative hypothesis is the one that must be supported. In other words, hypothesis testing is a way of determining whether the null hypothesis is reasonable or not.
The Type II error is defined as the error that occurs when the null hypothesis is not rejected even though it is incorrect. In hypothesis testing, this type of error is referred to as a beta error or a false-negative error. The chances of making a Type II error depend on several factors, including the sample size, the level of significance, and the power of the test. When the level of significance is lowered to 0.05, the chances of making a Type II error are 5%.
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For each of the following elementary matrices, describe the corresponding elementary row operation and write the inverse.
a. E = 1 0 3
0 1 0
0 0 1
b. E = 0 0 1
0 1 0
1 0 0
c. E = 1 0 0
0 1/2 0
0 0 1
d. E = 1 0 0
-2 1 0
0 0 1
e. E = 0 1 0
1 0 0
0 0 1
f. E = 1 0 0
0 1 0
0 0 5
In the given elementary matrix, the corresponding elementary row operation is multiplication of the second row of a given matrix with a scalar of 5. The given matrix is an elementary matrix because it can be obtained by multiplying an identity matrix by an elementary matrix. The inverse of the given matrix can be obtained by multiplying a scalar of 1/5 to the second row of the identity matrix.
The given elementary matrix is:
[1 0 0]
[0 0 5]
[0 1 0]
The corresponding elementary row operation for this matrix is multiplication of the second row of a given matrix with a scalar of 5. This means that if we have a matrix A and we multiply the second row of A with a scalar of 5, we get a new matrix B which is represented by the above elementary matrix.
The inverse of the given matrix is:
[1 0 0]
[0 1/5 0]
[0 0 1]
The inverse of a given elementary matrix can be obtained by applying the inverse of the corresponding elementary row operation to an identity matrix. In this case, the inverse of the given elementary matrix can be obtained by multiplying a scalar of 1/5 to the second row of the identity matrix. This gives us the above inverse matrix.
Therefore, the corresponding elementary row operation for the given matrix is multiplication of the second row of a given matrix with a scalar of 5 and the inverse of the given matrix is:
[1 0 0]
[0 1/5 0]
[0 0 1]
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An avid gardener wants to know which of two brands of fertilizer is best for her tomatoes. The two brands of fertilizer are A and B. She plants five pairs of tomato plants in two rectangular planters and places them beside one another. She gives each set of tomato plants the same amount of water each day, only she gives one set of plants fertilizer A and the other set of plants fertilizer B. At the end of the growing season, she counts the number of tomatoes each plant has yielded. Assume that all conditions for inference have been met. The rectangular planters are lined up so that plant 1 is beside plant 6, and plant 2 is beside plant 7, and so on. The yield for the five pairs of tomato plants are given. Plant 1 2 3 4 5 Yield with Fertilizer A 7 6 5 8 10 Plant 6 7 8 9 10 Yield with Fertilizer B 4 7 6 5 3 The gardener believes that fertilizer A enhances the yield of her tomatoes more than fertilizer B. She uses the following order of subtraction when determining the difference in the yields for the two brands: A- B (a) We would like to carry out a t test for the population mean difference. Calculate the point estimate. (b) Calculate the standard deviation of the differences. (Round your answer to three decimal places.) (c) Calculate the test statistic. (Round your answer to two decimal places.)
(a) Point estimate (mean difference): 2.2 tomatoes. (b) The standard deviation of differences: Approximately 3.47. (c) The test statistic: Approximately 1.38.
To perform a t-test for the population mean difference, follow these steps:
(a) Calculate the point estimate (mean difference): The point estimate is the mean difference between the yields of fertilizer A and fertilizer B.
Mean difference = (Sum of differences) / Number of pairs
Using the given data gives:
Mean difference = ((7-4) + (6-7) + (5-6) + (8-5) + (10-3)) / 5
Subtracting gives:
Mean difference = (3 - 1 - 1 + 3 + 7) / 5
Solving gives:
Mean difference = 11 / 5
Dividing gives:
Mean difference = 2.2
(b) Calculate the standard deviation of the differences:
To calculate the standard deviation of the differences, we need to calculate the squared differences, find their sum, divide by (n-1), and then take the square root.
Squared differences:[tex](3 - 2.2)^2, (-1 - 2.2)^2, (-1 - 2.2)^2, (3 - 2.2)^2, (7 - 2.2)^2[/tex]
Solving gives:
Sum of squared differences = (0.64 + 12.96 + 12.96 + 0.64 + 21.16)
Solving gives:
The sum of squared differences = 48.36
The standard deviation of the differences [tex]= \sqrt{48.36 / 4}[/tex]
Solving gives:
The standard deviation of the differences [tex]= \sqrt{2.09}[/tex]
Rounded to three decimal places
The standard deviation of the differences ≈ 3.47
c) Calculate the test statistic:
The test statistic (t) = (Point estimate - Null hypothesis value) / (Standard deviation /√(sample size))
Let's assume the null hypothesis is that there is no difference between the two fertilizers
(i.e., mean difference = 0).
[tex]t = (2.2 - 0) / (3.47 / \sqrt5)[/tex]
Substituting [tex]\sqrt 5 = 2.236[/tex]
t = 2.2 / (3.47 / 2.236)
Rounded to two decimal places
t ≈ 1.378
So, the test statistic is approximately 1.378.
The gardener can compare this test statistic to critical values from the t-distribution to determine whether the difference between the two fertilizers is statistically significant at a certain significance level. If the calculated test statistic is greater than the critical value, she ma
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PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP AND BE CORRECT
Answer:
The perimeter is the sum of the lengths of all the sides of a polygon. Thus, the perimeter of this quadrilateral is:
(10a-6) + (7a+4) + (7a+4) + (10a-6)
Simplifying the expression:
= 34a - 4
Therefore, the perimeter of the quadrilateral is 34a - 4.
please help me I have attached a photo below. thanks for your time
Therefore, the slope of the line passing through the points (0,5) and (2,0) is -5/2.
What is slope?In mathematics, slope refers to the measure of steepness of a line. It is the ratio of the change in y (vertical change) over the change in x (horizontal change) between any two points on the line. The slope of a line is represented by the letter "m" and can be calculated using the slope formula: m = (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are the coordinates of two points on the line.
Here,
To find the slope of a line, we use the formula:
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are any two points on the line.
Using the given coordinates, we have:
x1 = 0, y1 = 5
x2 = 2, y2 = 0
slope = (0 - 5) / (2 - 0)
slope = -5/2
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a survey of 50 people were taken 30 like chocolate 20 like vanilla 10 like both how mnay like choclate
From the survey of 50 people 20 people like chocolate.
A survey was conducted with 50 people, out of which 30 liked chocolate, 20 liked vanilla, and 10 liked both. The question is asking how many people like chocolate.
To determine the number of people who like chocolate only, we subtract the number of people who like both flavors from the total number of people who like chocolate.
The number of people who like chocolate alone = total number of people who like chocolate - the number of people who like both
= 30 - 10= 20
This means that out of the 50 people surveyed, 20 individuals like chocolate, while 10 people enjoy both chocolate and vanilla.
Therefore, 20 people like chocolate.
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5 A bathtub contains 35.5 liters of water.
When the plug is removed, 5 liters of wate
drain from the bathtub each minute. How
many minutes will it take all of the water to
drain from the bathtub?
A 177.5
B 7.1
C 17.75
D 6.95. i cant find my answer
Answer:
Option B
Step-by-step explanation:
Using Proportionality, we get
Let x be the quantity of water in bathtub. Y be time it be removed.
By formula, x2/y2= k = x1/y1
x/y = 5/1(x1=5, y1= 1)[Given]
5x2= 35.5
35.5 = 5y2
=> y = 35.5/5 = 7.1 minutes
48 identical looking bags of lettuce were delivered to Circle J grocers. Unfortunately, 12 of these bags of lettuce are contaminated with listeria. Joe, from Joes Cafe randomly selects 4 bags of the lettuce for his cafe. Let X equal the number of the selected packets which are contaminated with listeria. a. How many possible ways are there to select the 4 out of 48 packets (order does not matter) without replacement? b. What is the probability thatX=0
c. What is the probability thatX=4? d. What is the probability thatx>2? e. What is the expected value ofX? f. What is the standard deviation ofX? g. What is the probability that X is smaller than its expected value?
h. What is the probability thatX=5?
Probability that X = 5:Since, Joe selects only 4 bags of lettuce. X can't be 5.P(X=5) = 0Hence, the probability that X = 0 is 0.3164 and the probability that X = 5 is 0.
The given problem can be solved using the concept of binomial distribution.
In the given question, there are 48 bags of lettuce out of which 12 bags are contaminated with listeria.
Joe selects 4 bags of lettuce. X is the random variable which represents the number of contaminated bags of lettuce selected by Joe. X can take values from 0 to 4. (as Joe selects only 4 bags).
Part A)Number of ways to select 4 bags of lettuce out of 48:This can be solved using the concept of combinations. The formula to calculate the number of combinations is[tex]:nCr = n! / r!(n-r)![/tex]Here, n = 48 and r = 4.
Number of ways = 48C4 = 194,580
Part B)Probability that X = 0:This can be calculated using the formula for the binomial distribution :
[tex]P(X = r) = nCr * p^r * q^(n-r)[/tex]
Here, p = probability of selecting contaminated bag = 12/48 = 0.25q = probability of selecting non-contaminated bag = 1-0.25 = 0.75Also, n = 4 and r = [tex]0P(X=0) = 4C0 * 0.25^0 * 0.75^4= 0.3164[/tex]
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In the given truss bridge, parallelograms ABCD and PQRS are congruent. If AB = 24 feet, what is PQ?
Answer:
D. 24 ft
Step-by-step explanation:
Congruent means equal. Since ABCD and PQRS are congruent they are the same.
Answer:
D
Step-by-step explanation:
Which expressions are equivalent to
6
�
−
18
ℎ
6g−18h6, g, minus, 18, h?
Choose 2 answers:
Choose 2 answers:
(Choice A)
(
�
−
3
)
⋅
6
(g−3)⋅6left parenthesis, g, minus, 3, right parenthesis, dot, 6
A
(
�
−
3
)
⋅
6
(g−3)⋅6left parenthesis, g, minus, 3, right parenthesis, dot, 6
(Choice B)
2
⋅
(
3
�
−
18
ℎ
)
2⋅(3g−18h)2, dot, left parenthesis, 3, g, minus, 18, h, right parenthesis
B
2
⋅
(
3
�
−
18
ℎ
)
2⋅(3g−18h)2, dot, left parenthesis, 3, g, minus, 18, h, right parenthesis
(Choice C)
3
(
2
�
−
6
ℎ
)
3(2g−6h)3, left parenthesis, 2, g, minus, 6, h, right parenthesis
C
3
(
2
�
−
6
ℎ
)
3(2g−6h)3, left parenthesis, 2, g, minus, 6, h, right parenthesis
(Choice D)
(
−
�
−
3
ℎ
)
(
−
6
)
(−g−3h)(−6)left parenthesis, minus, g, minus, 3, h, right parenthesis, left parenthesis, minus, 6, right parenthesis
D
(
−
�
−
3
ℎ
)
(
−
6
)
(−g−3h)(−6)left parenthesis, minus, g, minus, 3, h, right parenthesis, left parenthesis, minus, 6, right parenthesis
(Choice E)
−
2
×
(
−
3
�
+
9
ℎ
)
−2×(−3g+9h)minus, 2, times, left parenthesis, minus, 3, g, plus, 9, h, right parenthesis
E
−
2
×
(
−
3
�
+
9
ℎ
)
−2×(−3g+9h)
You can use the distributive property of multiplication over addition and the fact that 18 is thrice of 6.
The given expression is equivalent to
Option C) [tex]3(2g-6h)[/tex]Option E) [tex]-2\times(-3g+9h)[/tex]What are equivalent expressions?Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.
What is the distributive property of multiplication over addition?[tex]a(b+c)=a\times b+a\times c[/tex]
(remember that many times, when using letters or symbols, we hide multiplication and write two things which are multiplied, close to each other. As in [tex]2\times x=2x[/tex])
The given expression is [tex]6g-18h[/tex]
We know that we can write
[tex]6=2\times3[/tex]
[tex]18=2\times9=3\times6[/tex]
Thus,
[tex]6g-18h=6\times g-6\times 3h=6(g-3h)=-6(-g+3h)[/tex]
[tex]6g-18h=2\times 3g-2\times 9h=2(3g-9h)=-2(-3g+9h)[/tex]
[tex]6g-18h=3\times 2g-3\times 6h=3(2g-6h)=-3(-2g+9h)[/tex]
All of the above forms are obtained from the same expression without altering its value but only forms, so their simplified forms are same so they are equivalent expressions.
Thus,
The given expression is equivalent to
Option C) [tex]3(2g-6h)[/tex]Option E) [tex]-2\times(-3g+9h)[/tex]Learn more about equivalent expressions here:
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Answer:C & D
Step-by-step explanation:
The expression shown in red represents how many hockey pucks and hockey sticks come in one gym set. The expression shown in blue shows how many come in 3
sets.
Use the drop-down menus to complete the statements below to compare the values of the two expressions.
Answer:
three times
Step-by-step explanation:
What is the meaning of logarithm in math?
In mathematics, a logarithm is a mathematical operation that determines how many times a given number (known as the base) must be multiplied by itself to produce another given number.
Logarithms are used to simplify complex calculations involving exponents and to convert between exponential and logarithmic expressions.
The logarithm of a number x to a given base b is represented as logb(x). For example, log10(100) = 2 because 10 multiplied by itself twice equals 100.
Logarithms have a wide range of applications in various fields, including mathematics, physics, engineering, finance, and computer science. They are particularly useful in scientific calculations involving large numbers, where working with exponents can become cumbersome. Logarithms are also used in the study of exponential growth and decay, as well as in the analysis of data sets with a wide range of values.
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Salaries for teachers in a particular state have a mean of $ 52000 and a standard deviation of $ 4800. a. If we randomly select 17 teachers from that district, can you determine the sampling distribution of the sample mean? Yes If yes, what is the name of the distribution? normal distribution The mean? 52000 The standard error? b. If we randomly select 51 teachers from that district, can you determine the sampling distribution of the sample mean? ? If yes, what is the name of the distribution? The mean? The standard error? C. For which sample size would I need to know that population distribution of X, teacher salaries, is normal in order to answer? ? v d. Assuming a sample size of 51, what is the probability that the sampling error is within $1000. (In other words, the sample mean is within $1000 of the true mean.) e. Assuming a sample size of 51, what is the 90th percentile for the AVERAGE teacher's salary? f. Assuming that teacher's salaries are normally distributed, what is the 90th percentile for an INDIVIDUAL teacher's salary?
a. Yes, the sampling distribution of the sample mean is a normal distribution with a mean of $52000 and a standard error of $\frac{4800}{\sqrt{17}}$.
b. Yes, the sampling distribution of the sample mean is a normal distribution with a mean of $52000 and a standard error of $\frac{4800}{\sqrt{51}}$.
c. You would need to know that the population distribution of X, teacher salaries, is normal in order to answer the questions regarding any sample size.
d. Assuming a sample size of 51, the probability that the sampling error is within $1000 is approximately 0.84 or 84%.
e. Assuming a sample size of 51, the 90th percentile for the average teacher's salary is approximately $54488.
f. Assuming that teacher's salaries are normally distributed, the 90th percentile for an individual teacher's salary is approximately $56396.
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You ate 4/12 of the pizza your family bought for dinner. Your brother ate 3/12 of the pizza. Which equation represents the fraction of pizza both you and your brother ate?
Answer:
7/12 pizzas have been eaten
Step-by-step explanation:
3 + 4= 7
7/12
7-12=5
5 pizzas left
Find $\sin X,\ \sin Z,\ \cos X,\ $ and $\cos Z$. Write each answer as a simplified fraction and rounded to four decimal places
The result of each trigonometric functions are:
a) sin X = 7√149 / 149
b) sin Z = 10√149 / 149
c) cos X = 10√149 / 149
d) cos Z = 7√149 / 149
In a right triangle, the sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse, and the cosine of an angle is equal to the length of the adjacent side divided by the length of the hypotenuse. Using this trigonometric functions, we can calculate sin X, sin Z, cos X, and cos Z as follows
sin X = YZ / XZ = 7 / √149
cos X = XY / XZ = 10 / √149
sin Z = XY / XZ = 10 / √149
cos Z = YZ / XZ = 7 / √149
To simplify these fractions, we can rationalize the denominator by multiplying the numerator and denominator by √149:
sin X = 7√149 / 149
cos X = 10√149 / 149
sin Z = 10√149 / 149
cos Z = 7√149 / 149
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The given question is incomplete, the complete question is:
Find sin X, sin Z, cos X, and cos Z. Write each answer as a simplified fraction.
Elena is testing out a new studying method and wants to know if it works. She decides to compare her spelling test scores from last week and this week. On last week's test, Elena spelled 16 out of the 20 words correctly. On this week's test, she spelled 13 out of the 15 words correctly. On which test did Elena get a higher ratio of correctly spelled words to total words?
Answer:
To determine which test Elena got a higher ratio of correctly spelled words to total words, we need to calculate the ratio of correctly spelled words to total words for each test and compare them.
For last week's test, the ratio of correctly spelled words to total words is:
16/20 = 0.8
For this week's test, the ratio of correctly spelled words to total words is:
13/15 ≈ 0.867
Since 0.867 is greater than 0.8, Elena got a higher ratio of correctly spelled words to total words on this week's test. Therefore, the new studying method appears to be working better for Elena. However, it is important to note that a single comparison is not sufficient to draw a definitive conclusion about the effectiveness of the studying method, and it would be beneficial for Elena to continue tracking her performance over a longer period of time.
during the computer daze special promotion, a customer purchasing a computer and printer is given a choice of three free software packages. there are 8 different software packages from which to select. how many different groups of software packages can be selected?
Therefore, there are 336 different groups of software packages that can be selected from the 8 different software packages offered during the Computer Daze special promotion.
There are 8 different software packages to choose from during the Computer Daze special promotion. Since the customer purchasing a computer and printer is given a choice of 3 free software packages, this means that there are 336 different groups of software packages that can be selected.
To calculate this, the total number of possibilities can be found by using the formula nPr,
where n is the total number of choices, and r is the number of items chosen. This can be written as 8P3. 8P3 is equal to[tex]8x7x6 = 336.[/tex]
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plain why the statistic is misleading.
Wilson was 42 inches tall on Jan 1, 2000, and 51 inches tall on Jan 1, 2002. William was 5 feet tall on Jan 1, 2000, and 6 feet tall on Jan 1, 2002.
Conclusion: The difference between 42 and 51 is greater than the difference between 5 and 6, so Wilson grew more during one year.
Wilson and William were measured at various times, therefore drawing the inference that Wilson grew more over the course of a year than William is incorrect and the statistics is misleading.
What is descriptive statistics?Inferential statistics and descriptive statistics are two disciplines of statistics with distinct applications.
Summarizing and characterizing gathered data is the focus of descriptive statistics. It uses techniques including graphical presentations, measurements of variability, and measures of central tendency, such as mean, median, and mode (e.g., histograms, box plots). The purpose of descriptive statistics is to shed light on a sample's or population's properties, such as its distribution, dispersion, and shape.
Wilson and William were measured at various times, therefore drawing the inference that Wilson grew more over the course of a year than William is incorrect.
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1. how long is the hall which has a perimeter if 3480 cm and 300cm wide?
2. joe walks across the rotonda and travels 400meters, how many more meters will a car travel around it than the distance the pedestrian walk?
3.father will fence the rectangular yard with a length of 120m and a width of 100m,
how many meters of wire will her use for the fence?
Answer:
(3480 - 600)/2 = 1440cm
Step-by-step explanation:
alexis created the two-way frequency table from information she gathered by asking 88 teenagers about their last online shopping experience. own money parents' money total completed purchase 16 34 50 just looked 22 16 38 total 38 50 88 about what percent of the teenagers purchased something with their parents' money?
The percentage of the teenagers who purchased something with their parents' money can be calculated from the two-way frequency table. About 38.64% of the teenagers purchased something with their parents' money.
There were a total of 88 teenagers who were surveyed by Alexis. 38 of them completed the purchase, and out of these 38 teenagers, 34 of them used their parents' money. So, the percentage of teenagers who purchased something with their parents' money can be calculated as follows:
Percent of teenagers who purchased something with their [tex]parents' money = \frac{Frequency of completed purchase}{Total Number of teenagers surveyed} *100[/tex]
Percent of teenagers who purchased something with their parents' money = [tex]\frac{34}{88} * 100%[/tex]%
Therefore percent of teenagers who purchased something with their parents' money = 38.64%
Therefore, about 38.64% of the teenagers purchased something with their parents' money.
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which degenerate conic is formed when a double cone is sliced at the apex by a plane perpendicular to the base of the cone?
When a double cone is sliced at the apex by a plane perpendicular to the base of the cone, the resulting conic section is a parabola.
Option B is the correct answer.
We have,
A parabola is a type of conic sect ion that can be defined as the locus of points equidistant from a fixed point (the focus) and a fixed line (the directrix).
In the case of slicing a double cone at the apex, the resulting conic section will have the characteristic shape of a parabola.
The slicing plane intersects both sides of the double cone, creating a curved shape that opens upward or downward, depending on the orientation of the cone.
The vertex of the parabola corresponds to the point of intersection of the slicing plane with the double cone.
Therefore,
When a double cone is sliced at the apex by a plane perpendicular to the base, a parabola is formed.
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The complete question:
Which degenerate conic is formed when a double cone is sliced at the apex by a plane perpendicular to the base of the cone?
A. Circle
B. Parabola
C. Ellipse
D. Hyperbola
Please help, due very soon !!
Use the quadratic formula to solve. Show work describe solution.
Answer:
Use the quadratic formula to solve. Show work describe solution.
Step-by-step explanation:
The quadratic formula is used to find the solutions (or roots) of a quadratic equation in the form ax^2 + bx + c = 0, where a, b, and c are constants.
The quadratic formula is:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
To use the quadratic formula, we need to plug in the values of a, b, and c from the given equation and solve for x.
For example, let's say we have the equation 2x^2 + 5x - 3 = 0.
Here, a = 2, b = 5, and c = -3.
Plugging these values into the quadratic formula, we get:
x = (-5 ± sqrt(5^2 - 4(2)(-3))) / 2(2)
Simplifying the expression inside the square root:
x = (-5 ± sqrt(49)) / 4
x = (-5 ± 7) / 4
We get two solutions:
x = (-5 + 7) / 4 = 1/2
x = (-5 - 7) / 4 = -3
So the solutions to the equation 2x^2 + 5x - 3 = 0 are x = 1/2 and x = -3.
These solutions represent the points where the quadratic curve intersects the x-axis. They can also be used to factor the quadratic equation or graph the quadratic function.
A chemist has 20% and 50% solutions of acid available. How many liters of each solution should be mixed to obtain 600 liters of 21% acid solution?
[tex]x=\textit{Liters of solution at 20\%}\\\\ ~~~~~~ 20\%~of~x\implies \cfrac{20}{100}(x)\implies 0.2 (x) \\\\\\ y=\textit{Liters of solution at 50\%}\\\\ ~~~~~~ 50\%~of~y\implies \cfrac{50}{100}(y)\implies 0.5 (y) \\\\\\ \textit{600 Liters of solution at 21\%}\\\\ ~~~~~~ 21\%~of~600\implies \cfrac{21}{100}(600)\implies 126 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{array}{lcccl} &\stackrel{Liters}{quantity}&\stackrel{\textit{\% of Liters that is}}{\textit{acid only}}&\stackrel{\textit{Liters of}}{\textit{acid only}}\\ \cline{2-4}&\\ \textit{1st Sol'n}&x&0.2&0.2x\\ \textit{2nd Sol'n}&y&0.5&0.5y\\ \cline{2-4}&\\ mixture&600&0.21&126 \end{array}~\hfill \begin{cases} x + y = 600\\\\ 0.2x+0.5y=126 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{using the 1st equation}}{x+y=600}\implies x=600-y \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{0.2(600-y)+0.5y=126}\implies 120-0.2y+0.5y=126 \\\\\\ 120+0.3y=126\implies 0.3y=6\implies y=\cfrac{6}{0.3}\implies \boxed{y=20} \\\\\\ \stackrel{\textit{since we know that}}{x=600-y}\implies \boxed{x=580}[/tex]
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Write the equation of the circle using the center and any one of the given points A, B, or C
Answer:
To write the equation of a circle given its center and a point on the circle, we need to use the standard form of the equation of a circle, which is:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) is the center of the circle and r is the radius.
Let's use point A as the point on the circle. We are given that the center of the circle is (4, -2) and point A is (6, 1). We can use the distance formula to find the radius of the circle:
r = √[(6 - 4)^2 + (1 - (-2))^2] = √[4^2 + 3^2] = 5
Now we can substitute the center and radius into the standard form equation:
(x - 4)^2 + (y + 2)^2 = 5^2
Simplifying and expanding the right-hand side, we get:
(x - 4)^2 + (y + 2)^2 = 25Therefore, the equation of the circle is (x - 4)^2 + (y + 2)^2 = 25 and we used point A to find it.
The perimeter of a rectangle is 112 cm and its 10. A group
The tota
breadth is x cm.
(i) Find, in terms of x, an expression for the
length of the rectangle.
(ii) Given that the area of the rectangle is 597 cm²,
formulate an equation in x and show that it
reduces to x²-56x +597 = 0.
(iii) Solve the equation x²-56x + 597 = 0, giving
both answers correct to 2 decimal places.
(iv) Hence, find the length of the diagonal of
the rectangle.
Therefore, the length of the diagonal of the rectangle is approximately 193.57 cm or 49.43 cm, depending on which value of x is used.
What is perimeter?Perimeter is the total distance around the edge of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape. For example, the perimeter of a rectangle is found by adding the lengths of its four sides.
Here,
(i) Let the length of the rectangle be y cm.
Then, the perimeter of the rectangle is given by:
2(x + y) = 112
x + y = 56
y = 56 - x
(ii) The area of the rectangle is given by:
Area = length x breadth
597 = yx
Substituting y = 56 - x, we get:
597 = x(56 - x)
597 = 56x - x²
x² - 56x + 597 = 0
(iii) Using the quadratic formula,
x = (-(-56) ± √((-56)² - 4(1)(597))) / (2(1))
x = (56 ± √(3136 - 2388)) / 2
x = (56 ± √(748)) / 2
x = (56 ± 2√(187)) / 2
x = 28 ± √(187)
Therefore, the two solutions are x = 28 + √(187) and x = 28 - √(187).
(iv) The length of the rectangle is y = 56 - x.
Using Pythagoras theorem, the length of the diagonal of the rectangle is given by:
d² = y² + x²
d² = (56 - x)² + x²
d² = 3136 - 112x + 2x²
d = √(3136 - 112x + 2x²)
Substituting the value of x from part (iii) into the above equation, we get:
d = √(3136 - 112(28 ± √(187)) + 2(28 ± √(187))²)
d = √(3136 - 3136 ± 112√(187) + 56 ± 56√(187) + 2(187))
d = √(37400 ± 168√(187))
d ≈ 193.57 cm (rounded to 2 decimal places) or d ≈ 49.43 cm (rounded to 2 decimal places)
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Solve the triangle MNO (find the measure of ∠O and the lengths of sides MO and NO).
(I need help finding both side measures and angle measure please and thank you
Answer:
Step-by-step explanation:
m∠O = 90° - 34° = 56°
cos M = [tex]\frac{MN}{MO}[/tex] ⇒ MO = [tex]\frac{12}{cos34}[/tex] ≈ 14.5 cm
tan M = [tex]\frac{ON}{MN}[/tex] ⇒ ON = 12 × tan 34° ≈ 8.1 cm
What is an equation of the line that passes through the points ( 3 , 6 ) (3,6) and ( − 1 , − 6 ) (−1,−6)?
Answer:
y = 3x - 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (3, 6 ) and (x₂, y₂ ) = (- 1, - 6 )
m = [tex]\frac{-6-6}{-1-3}[/tex] = [tex]\frac{-12}{-4}[/tex] = 3 , then
y = 3x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (3, 6 )
6 = 3(3) + c = 9 + c ( subtract 9 from both sides )
- 3 = c
y = 3x - 3 ← equation of line
C. Use Structure Why might Tavon have chosen
to multiply both sides of the equation by 10?
Could he have used another number? Explain.
By answering the presented question, we may conclude that In general, expressions it is often most convenient to choose numbers that are powers of ten.
what is expression ?In mathematics, an expression is a collection of integers, variables, and complex mathematical (such as arithmetic, subtraction, multiplication, division, multiplications, and so on) that describes a quantity or value. Phrases can be simple, such as "3 + 4," or complicated, such as They may also contain functions like "sin(x)" or "log(y)". Expressions can be evaluated by swapping the variables with their values and performing the arithmetic operations in the order specified. If x = 2, for example, the formula "3x + 5" equals 3(2) + 5 = 11. Expressions are commonly used in mathematics to describe real-world situations, construct equations, and simplify complicated mathematical topics.
Tavon may have chosen to multiply both sides of the equation by 10 because he wanted to remove the decimal point and work with integers. Then he can use his knowledge of integer multiplication and division to solve the equations more easily.
Tavon may have used a different number and removed the decimal point. For example, you could multiply both sides by 100 or 1000 instead of 10. However, you should carefully choose a number that is manageable and does not overcomplicate the problem. Multiplying by larger numbers complicates the calculations, and multiplying by smaller ones does not eliminate the decimal point entirely. In general, it is often most convenient to choose numbers that are powers of ten.
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