Using the volume of a cylinder the amount of broth used is 565 cm³
What is the volume of a cylinder?The volume of a cylinder is given by V = πr²h where
r = radius of cylinder and h = height of cylinderNow, since a brand new filled can of chicken broth is 9 cm tall and has a radius of 6 cm. Mishka uses some of the broth to cook and now the broth left in the can is 4 cm high.
To determine how much broth did Mishka use, we proceed as follows.
We know that the can is a cylinder so its volume is V = πr²h where
r = radius of cylinder and h = height of cylinderNow, the volume of broth used is the difference in height between the height of the cyliner and the height of the amount of broth left.
So, V = πr²(H - h) where
r = radius of cylinderH = height of cylinder and h = height of amount of broth leftGiven that
r = 6 cmH = 9 cm and h = 4 cmSubstituting the values of the variables into the equation, we have that
V = πr²(H - h)
V = π(6 cm)²(9 cm - 4 cm)
= π(36 cm²)(5 cm)
= 180π cm³
= 565.4 cm³
≅ 565 cm³
So, the amount used is 565 cm³
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Please help me on this.
Answer:
B No solution
Step-by-step explanation:
one day, a downtown hotel in san jose had to walk a guest to another hotel. the room rate for another hotel in downtown was $150. it cost $15 for the guest to take an uber to another hotel. the overbooked hotel also gave the guest a gift card of $25. how much is the cost of walking this guest? group of answer choices $150 $180 $190 $160
The cost of walking this guest is $190.
The cost of walking the guest can be calculated by adding up the expenses incurred by the hotel.
The guest was walked to another hotel that charged a room rate of $150. Therefore, the hotel incurred a cost of $150 for the room.
In addition to the room cost, the hotel also paid for the guest's Uber ride to the new hotel, which was $15.
Furthermore, the overbooked hotel gave the guest a gift card worth $25. Although the gift card does not directly represent an expense, it can be considered as an opportunity cost for the hotel, as they could have used that money to cover other costs.
Therefore, the total cost incurred by the hotel for walking the guest is:
$150 (room cost) + $15 (Uber cost) + $25 (gift card cost) = $190
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The article referenced in this lesson also stated that the pig landed on its right side lesson also stated that the pig landed on its right side 4,172 times out of 11,954 tosses. You will construct a 90% confidence interval for the population proportion of tosses of a plg die in which the pig lands on A Are the criteria for approximate normality met? es of a pig die in which the pig lands on its right side. B Find the sample proportion and the critical value: 0571 and Z= C Find the estimated standard error, SA, and compute the margin of error, m. 0349U-2349) = 0,004 11,954 m=2 si: 2x 0,004 -0.008 D Find the 90% confidence interval. Provide an interpretation of the confidence interval in context of this problem. E Would you support the claim that 33% of all tosses have the pig landing on its right side? Explain your reasoning. F What is the best way to decrease the margin of error and create a more precise estimate for the population proportion? Why would you want a smaller margin of error? G If you were to compute the 99% confidence interval, would it be wider or narrower than the 90% confidence interval? Explain briefly.
To determine if the criteria for approximate normality is met, we need to check if both the sample size and sample proportion are large enough. The sample size is n = 11,954 which is greater than 10.
Additionally, the sample proportion of landing on its right side is p = 0.571 which is also greater than 10. Therefore, the criteria for approximate normality is met.
A 99% confidence interval would be wider than the 90% confidence interval. This is because a higher confidence level requires a larger range to ensure the true population proportion is captured within the interval with a higher degree of certainty.
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Julie was assigned to take her statistics class with Professor Fisher, whose final scores follow a normal distribution with mean 75
and a standard deviation of 6
. Her score on the final was 84
.
What is Julie's z-score?
Julie's z-score is 1.5. This means that her score on the final was 1.5 standard deviations above the mean score of the class.
What is the mean and standard deviation?
The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.
To calculate Julie's z-score, we need to use the formula:
z = (x - μ) / σ
where:
x is Julie's score on the final (84)
μ is the mean score of the class (75)
σ is the standard deviation of the class (6)
Plugging in the values, we get:
z = (84 - 75) / 6
z = 1.5
Therefore, Julie's z-score is 1.5. This means that her score on the final was 1.5 standard deviations above the mean score of the class.
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determine if the function is an exponential function
f (x) = x^3
Answer:
Yes, the function is exponential.
Step-by-step explanation:
The "^" represents an exponet. If you want to know, the exponent is 3.
a sample obtained in such a way that every element in the population has an equal chance of being selected is
A sample obtained in such a way that every element in the population has an equal chance of being selected is called a random sample.
In a random sample, each member of the population is selected independently and randomly, which means that each member has an equal chance of being included in the sample. Random sampling is a fundamental method used in statistical analysis, and it helps ensure that the sample is representative of the population.
By obtaining a representative sample, we can draw accurate conclusions about the population and make statistical inferences with confidence. Common methods of random sampling include simple random sampling, stratified sampling, and cluster sampling, among others.
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Complete Question:
a sample obtained in such a way that every element in the population has an equal chance of being selected is __.
What is the surface area of the triangular prism.
Answer:480cm^3
Step-by-step explanation:
In a survey, students are asked how many hours they study in a typical week. A five-number summary of the responses is: 2, 9, 14, 20, 60. Which interval does not describe the number of hours spent studying in a typical week for about 50% of the students sampled?
The interval that does not describe the number of hours for about 50 % of the students is B. 9 to 14.
How to find the interval ?In order to gain a proper insight into the dataset, a holistic five-number summary is employed that accounts for the minimum value, first quartile (Q1), median, third quartile (Q3), and maximum value. Of these key components, Q1 defines the 25th percentile of the data while Q3 exhibits the 75th percentile.
As it stands, the median of this particular collection - 14 - denotes that half of the students are studying for less than 14 hours per week and the other half above the same timeframe.
This means that the interval that does not show 50 % would be 9 - 14 as this only shows 25 %.
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Options include:
A. 9 - 20
B. 9 - 14
C . 2 - 14
another social worker, who works at a community development organization, makes a different claim. they claim that the average number of children who drop out of high school each day in a particular city is different than 15 children. they would like to carry out a hypothesis test and test the claim that the average number of children who drop out of high school each day in a particular city is different than 15 children. why is this hypothesis test two-tailed? select the correct answer below: this is a two-tailed test because no direction is specified. this is a two-tailed test because a direction is specified. the population parameter is greater than the specified value. this is a two-tailed test because a direction is specified. the population parameter is less than the specified value. more information is needed.
This hypothesis test is two-tailed because no direction is specified in the claim made by the social worker.
A two-tailed test means that the alternative hypothesis is that the population parameter is different from the specified value (in this case, 15 children dropping out of high school each day). So, the null hypothesis would be that the population parameter is equal to 15, while the alternative hypothesis would be that it is either greater than or less than 15. Therefore, we need to conduct a two-tailed test to determine whether the social worker's claim is statistically significant. The correct answer to your question is: This is a two-tailed test because no direction is specified.
In this scenario, the social worker at the community development organization wants to test the claim that the average number of children who drop out of high school each day in a particular city is different than 15 children. The hypothesis test is two-tailed because there is no specified direction for the population parameter (whether it's greater than or less than 15 children). Instead, the test simply seeks to determine if the average number of dropouts is different from 15, which could be in either direction.
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Which expressions are equivalent to 6 +(–x) + 2x + (–7) + 2x? Check all that apply.
A. x + x + 6 – 7 + x
B. 2x + 2 + x
C. 3 – x + 2x – 4 + 2x
D. x – 1
E. x + 1
(The answer is A and C)
The expressions are equivalent to the given expression are x + x + 6 – 7 + x and 3 – x + 2x – 4 + 2x. Therefore, the options A and C are correct answer.
The given expression is 6+(-x)+2x+(-7)+2x.
If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
Here, group the like terms, we get
(-x+2x+2x)+(6-7)
= 3x-1
Therefore, the options A and C are correct answer.
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Answer:
yo
Step-by-step explanation:
the answers are A and C
x + x + 6 – 7 + x and 3 – x + 2x – 4 + 2x
Edge 2023
the table below shows the number of survey subjects who have received and not received a speeding ticket in the last year, and the color of their cars. speeding ticket no speeding ticket total red car 141 194 335 not red car 200 89 289 total 341 283 624 find the probability that a randomly chosen person: a) has a red car. b) has a speeding ticket. c) has a speeding ticket given they have a red car. d) has a red car given they have a speeding ticket. e) has a red car and got a speeding ticket. f) has a red car or got a speeding ticket. write your answers in decimal form, rounded to the nearest thousandth.
Therefore, the required probabilities are:
a) P(red car) = 0.537
b) P(speeding ticket) = 0.546
c) P(speeding ticket | red car) = 0.421
d) P(red car | speeding ticket) = 0.413
e) P(red car and speeding ticket) = 0.226
f) P(red car or speeding ticket) = 0.857
a) The probability that a randomly chosen person has a red car is the number of people with red cars divided by the total number of people, which is:
P(red car) = 335/624
= 0.537 (rounded to the nearest thousandth).
b) The probability that a randomly chosen person has a speeding ticket is the number of people with speeding tickets divided by the total number of people, which is:
P(speeding ticket) = 341/624
= 0.546 (rounded to the nearest thousandth).
c) The probability that a randomly chosen person has a speeding ticket given they have a red car is the number of people with red cars and speeding tickets divided by the number of people with red cars, which is:
P(speeding ticket | red car) = 141/335
= 0.421 (rounded to the nearest thousandth).
d) The probability that a randomly chosen person has a red car given they have a speeding ticket is the number of people with red cars and speeding tickets divided by the number of people with speeding tickets, which is:
P(red car | speeding ticket) = 141/341
= 0.413 (rounded to the nearest thousandth).
e) The probability that a randomly chosen person has a red car and got a speeding ticket is the number of people with red cars and speeding tickets divided by the total number of people, which is:
P(red car and speeding ticket) = 141/624
= 0.226 (rounded to the nearest thousandth).
f) The probability that a randomly chosen person has a red car or got a speeding ticket is the sum of the probabilities of having a red car and having a speeding ticket minus the probability of having both, which is:
P(red car or speeding ticket) = P(red car) + P(speeding ticket) - P(red car and speeding ticket)
= 0.537 + 0.546 - 0.226
= 0.857 (rounded to the nearest thousandth).
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if the vertex of a parabola is (5,-10) what is the axis of symmetry?
The axis of symmetry of a parabola with vertex (5, -10) is x = 5, which is a vertical line passing through the vertex.
The axis of symmetry of a parabola is a vertical line that passes through its vertex and divides the parabola into two mirror-image halves. In this case, the vertex of the parabola is given as (5, -10), which means the vertex lies on a horizontal line passing through the axis of symmetry.
The equation of the axis of symmetry can be written as x = h, where (h, k) is the vertex of the parabola.
As from the given points h corresponds to value '5'. Therefore, the axis of symmetry for this parabola is x = 5, which is a vertical line passing through the point (5, -10).
To visualize this, you can imagine folding the parabola along its axis of symmetry. The left and right halves of the parabola will overlap perfectly, creating a symmetrical shape.
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The distinction between real variables and nominal variables is known as.
The distinction between real variables and nominal variables is based on the type of measurement used to represent the variable.
A variable is a characteristic that can take different values or levels. Real variables are measured on a numerical scale and can take any value within a certain range.
On the other hand, nominal variables are categorical variables that represent non-numerical attributes. They are used to classify data into different groups or categories based on their characteristics. Examples of nominal variables include gender, race, nationality, and occupation. These variables cannot be measured using a numerical scale, but they can be represented using labels or codes.
The distinction between real variables and nominal variables is important because they require different methods of analysis. Real variables can be analyzed using statistical methods such as mean, standard deviation, and correlation, while nominal variables require different methods such as frequency tables and chi-square tests.
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the ratio of union members to nonunion members working for a company is 4 to 5. if there are employees total, 207 how many union members work for the company?
There are 662 union members working for the company.
What is proportion?
The size, number, or amount of one thing or group as compared to the size, number, or amount of another. The proportion of boys to girls in our class is three to one.
Let's use "x" to represent the ratio multiplier, which will allow us to find the actual number of union and nonunion members.
According to the problem, the ratio of union members to nonunion members is 4 to 5. This means that for every 4 union members, there are 5 nonunion members.
We can set up a proportion to find the value of x:
4/5 = x/207
To solve for x, we can cross-multiply:
4 × 207 = 5 * x
828 = 5x
x = 828/5
x = 165.6
Since we cannot have a fraction of a person, we must round this value to the nearest whole number.
Now we can use x to find the actual number of union members:
Number of union members = 4x
Number of union members = 4 × 165.6
Number of union members = 662.4
hence, Rounding this value to the nearest whole number, we can say that there are 662 union members working for the company.
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The line L is normal to the curve defined by 2xy2 -3y = 18 at the point (3,2). The slope of line L is:
(A) 21/8 (B) 32/3 (C) - 10/21 (D) 8/21 (E) - 8/21
Slope of the normal L is 21/8.
Hence the correct option is (A).
Slope of normal to a function f(x) = y is given by = -dx/dy
Given the equation of the curve is,
2xy² - 3y = 18
Differentiating the function with respect to 'x' we get,
2x*2y*dy/dx + 2y²*1 - 3 dy/dx = 0
4xy*dy/dx + 2y² - 3dy/dx = 0
(3 - 4xy)dy/dx = 2y²
dy/dx = 2y²/(3 - 4xy)
-dx/dy = (4xy - 3)/2y²
Slope of the normal L at the point (3, 2) = (4*3*2 - 3)/(2*2²) = (24 - 3)/8 = 21/8
Hence the correct option is (A).
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the probability of winning a certain lotter is 1/51,949. for people who play 560 times, find the standard deviation for the random variable x, the number of wins
The standard deviation for the random variable X, the number of wins, is approximately 0.10341.
Probability of winning a certain lottery [tex]= 1/51,949[/tex]
560 times were played overall.
Let X represent the random variable that represents the number of victories out of 560 plays.
The probability of winning in one play is [tex]p = 1/51,949[/tex]. The probability of not winning in one play is [tex]q = 1 - p[/tex]
[tex]q = (51,949 - 1) / 51,949[/tex]
[tex]q = 51,948 / 51,949.[/tex]
What X should actually be is:
[tex]E(X) = np[/tex]
[tex]E(X) = 560 * (1/51,949)[/tex]
[tex]E(X) = 0.010793[/tex]
The variance of X is:
[tex]Var(X) = npq[/tex]
[tex]Var(X) = 560 * (1/51,949) * (51,948/51,949)[/tex]
[tex]Var(X) = 0.010699[/tex]
The value of X's standard deviation is
[tex]SD(X) = \sqrt{Var(X)}[/tex]
[tex]SD(X) = \sqrt{0.010699}[/tex]
[tex]SD(X) = 0.10341[/tex](approx)
Therefore, the standard deviation for the random variable X, the number of wins, is approximately 0.10341.
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Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = ln 3x, y = 2, y = 3, x= 0; about the y-axis
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 9x^6, y = 9x, x greaterthanorequalto 0; about the x-axis
The volume of solid generated by rotating the region bounded by curves y = ln( 3x), y = 2, y = 3, x= 0; about the y-axis is equals to the [tex] \frac{π}{18}({e^6}- e^4)[/tex]. The volume of solid generated by rotating the region bounded by curves = 9x⁶, y = 9x, x ≥0; about x-axis is equals to the [tex]\frac{81π}{13} \\ [/tex].
We have a solid obtained by rotating the region bounded by the curves with equations, y = ln 3x, y = 2, y = 3, x= 0; about the specified line, y-axis. We have to determine the volume, V of that solid. First, see the above diagram where red line, green line, blue line and purple lines represent y = ln 3x, y = 3, y = 2, x= 0 respectively. The volume of shaded region will be determine. Using formula, [tex]V = \int_{y = 2}^{y = 3} πx² dy \\ [/tex]
Now, y = ln( 3x)
taking exponential both sides,
[tex]e^ y = 3x [/tex]
[tex]x = \frac{ e^y}{3}[/tex]
so, [tex]V = \int_{y = 2}^{y = 3} π ( \frac{e^y}{3})² dy \\ [/tex]
[tex]= \int_{y = 2}^{y = 3} π ( \frac{e^{2y}}{9})dy \\ [/tex]
[tex]=[π(\frac{e^{2y}}{9 \times 2})]_{2}^{3} [/tex]
[tex]= π ( \frac{e^6}{18} -\frac{ e^4}{18})[/tex]
[tex]= \frac{π}{18}({e^6}- e^4)[/tex]
Hence, required value is [tex]= \frac{π}{18}({e^6}- e^4)[/tex].
Solid obtained by rotating the region bounded by the curves with equations, y = 9x⁶, y = 9x, x ≥0; about the specified line, x-axis. We have to determine the volume, V of that solid. First we determine the intersection points of y = 9x² and y = 9x
=> 9x = 9x²
=> x = 1
Using the formula, [tex]V = \int_{x= 0}^{x = 1} πy² dx \\ [/tex]
[tex] = \int_{x= 0}^{x = 1} π(9x⁶)² dx \\ [/tex]
[tex] = \int_{x= 0}^{x = 1} 81πx¹² dx \\ [/tex]
[tex] = 81π [ \frac{x¹³}{13}]_{x= 0}^{x = 1} \\ [/tex]
[tex] = 81π [ \frac{1¹³}{13} - 0] \\ [/tex]
[tex] = \frac{81π}{13} \\ [/tex]. Hence, required value is [tex]\frac{81π}{13} \\ [/tex].
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What is the median of this data set?
Rainfall (in inches)
Answer:
2, 3, 1, 3, 5, 4---->1, 2, 3, 3, 4, 5
The median is 3.
A fair coin is tossed 10 times. If is the number of times that heads is tossed, what is P(3<≤6)?
The probability of P(3 < X ≤ 6) is approximately 0.6575.
What is probability?The study of probabilities, which are determined by the ratio of favourable occurrences to probable cases, is known as probability.
To find P(3 < X ≤ 6), where X represents the number of times heads is tossed when a fair coin is tossed 10 times, we need to calculate the probability of obtaining more than 3 but less than or equal to 6 heads.
Since the coin is fair, the probability of getting heads on any single toss is 0.5, and the probability of getting tails is also 0.5.
We can use the binomial probability formula to calculate the probability for a specific number of heads in a given number of coin tosses:
P(X = k) = (n choose k) * [tex]p^k[/tex] *[tex](1-p)^{(n-k)[/tex],
where n is the number of trials, k is the number of successful outcomes, p is the probability of success on each trial, and (n choose k) is the binomial coefficient.
In this case, n = 10 (10 coin tosses), p = 0.5 (probability of heads), and we want to calculate the probability for 4, 5, and 6 heads.
P(3 < X ≤ 6) = P(X = 4) + P(X = 5) + P(X = 6)
Using the binomial probability formula, we can calculate these probabilities:
P(X = 4) = (10 choose 4) * [tex](0.5^4) * (0.5^6)[/tex] = 210 * 0.0625 * 0.015625 = 0.2063
P(X = 5) = (10 choose 5) * [tex](0.5^5) * (0.5^5)[/tex] = 252 * 0.03125 * 0.03125 = 0.2461
P(X = 6) = (10 choose 6) * [tex](0.5^6) * (0.5^4)[/tex] = 210 * 0.015625 * 0.0625 = 0.2051
Finally, we can calculate the desired probability:
P(3 < X ≤ 6) = P(X = 4) + P(X = 5) + P(X = 6) = 0.2063 + 0.2461 + 0.2051 = 0.6575
Therefore, P(3 < X ≤ 6) is approximately 0.6575.
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What is the simplified form of the following expression? Assume x > 0.
3
2x
4/6x
O2x
√24x3
2x
24x3
16x4
O√12x²
The simplified form of expression [tex]\sqrt[4]{\frac{3}{2x} }[/tex] is [tex]\frac{\sqrt[4]{24 x^3}}{2x }[/tex]
The correct answer is an option (B)
Consider an expression [tex]\sqrt[4]{\frac{3}{2x} }[/tex]
Multiply the fraction by an expression to form a perfect square in the denominator.
[tex]\sqrt[4]{\frac{3}{2x} }[/tex]
[tex]=\sqrt[4]{\frac{3\times 2^3\times x^3}{2x\times 2^3\times x^3} }[/tex]
We know that the cube of 2 is 8. So, substitute 2³ = 8
[tex]=\sqrt[4]{\frac{3\times 8\times x^3}{2x\times 8\times x^3} }[/tex]
Now, we multiply the monomials.
[tex]=\sqrt[4]{\frac{24\times x^3}{16\times x^4} }[/tex]
We know that the exponent rule [tex](a\times b)^m=a^m\times b^m[/tex]
[tex]=\frac{\sqrt[4]{24\times x^3}}{\sqrt[4]{16\times x^4} }[/tex]
We know that 2⁴ = 16
[tex]=\frac{\sqrt[4]{24\times x^3}}{\sqrt[4]{2^4\times x^4} }\\\\=\frac{\sqrt[4]{24\times x^3}}{\sqrt[4]{2^4}\times \sqrt[4]{x^4} }[/tex] ............(using the exponent rule [tex](a\times b)^m=a^m\times b^m[/tex])
[tex]=\frac{\sqrt[4]{24\times x^3}}{2x }[/tex] .......(Simplify the radical expressions)
Here, [tex]\frac{\sqrt[4]{24 x^3}}{2x }[/tex] is the simplified form of expression.
Therefore, the correct answer is an option (B)
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Find the complete question below.
Do scores on a test of math achievement exceed the recommended minimum of 76% for eighth-graders in Maryland?Choose the correct inference procedure to answer this question
This inference procedure allows you to compare the sample mean to the recommended minimum and determine if there is a statistically significant difference.
To answer this question, we would use a hypothesis test. Specifically, we would set up a null hypothesis that the average math achievement score for eighth-graders in Maryland is equal to or less than 76%, and an alternative hypothesis that the average score exceeds 76%.
We would then collect a sample of math achievement scores from eighth-graders in Maryland and use a t-test or z-test to determine if the sample mean is significantly different from 76%.
To answer the question of whether eighth-graders in Maryland exceed the recommended minimum of 76% on a test of math achievement, you should use a one-sample t-test. This inference procedure allows you to compare the sample mean to the recommended minimum and determine if there is a statistically significant difference.
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Which is smallest?
0.2, 0.019, 0.12, 0.02
From the given decimals which are 0.2, 0.019, 0.12, 0.02, the smallest number is 0.019.
To compare the given decimals, we need to look at the digits to the right of the decimal point. Starting from the left, the first decimal is 0.2, which has one decimal place. The second decimal is 0.019, which has three decimal places. The third decimal is 0.12, which has two decimal places. Finally, the fourth decimal is 0.02, which has two decimal places.
To compare them, we can line them up vertically by decimal place and see which one has the smallest value in the first decimal place. In this case, the smallest value in the first decimal place is 0.019. Therefore, 0.019 is the smallest decimal among the given options.
In summary, the decimals listed from smallest to largest are: 0.019, 0.02, 0.12, 0.2.
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Spin a spinner with three equal sections colored red, white, and blue. What is P(yellow)?
33%
0%
100%
66%
In a case whereby there is a spinner with three equal sections colored red, white, and blue the P(yellow) is 33%
What is probability?Probability can be described as trhe act of showing how likely something is to happen it should be noted that this usually comes into play when we were not sure about the outcome of an event, and the analysis of events governed by probability can be regarded as statistics.
P(yellow) = 1/3
= 0.33
0.33 * 100
= 33 percent
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You are buying a car whose price is $22,500. Which of the following options will
you choose? Explain.
a. You are given a factory rebate of $2000, followed by a dealer discount of 10%.
b. You are given a dealer discount of 10%, followed by a factory rebate of $2000.
Let f(x) = x-2000 and let g(x) = .9x Which option is represented by thecomposite f(g(x))? Which option is represented by the composite g(f(x)) ?
The best option for the car deal is option B.
The composite function represented by g(f(x)) = 0.9(x - 2000), is option a.
What is the best possible deal for the car?The best possible deal for the car is determined from the final price in each case.
If you apply $2000 first, then the price becomes
= $22,500 - $2000
= $20,500
Then apply 10% discount, the final price becomes;
= (100% - 10%) x $20,500
= 0.9 x $20,500
= $18,450
For option b, we will apply the 10% discount first,;
= (100% - 10%) x $22,500
= 0.9 x $22,500
= $ 20,250
The apply a rebate of $2000, the final price becomes;
= $ 20,250 - $2,000
= $18,250
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26
In the xy-plane, a parabola has vertex (9,-14) and
intersects the x-axis at two points. If the equation of
the parabola is written in the form y = ax²+bx+c₁
where a, b, and c are constants, which of the
following could be the value of a +b+c?
A) -23
B) -19
C) -14
D) -12
The possible values of the sum of a, b and c is (c) - 14
Calculating the possible values of the sum of a, b and cFrom the question, we have the following parameters that can be used in our computation:
Vertex = (9, -14)
It intersects the x-axis at two points.
So, we have (x₁, 0) and (x₂, 0)
The equation of a parabola in vertex form is represented as
y = a(x - h)² + k
Where
Vertex = (h, k)
So, we have
y = a(x - 9)² - 14
Expanding the equation, we have
y = a(x² - 18x + 81) - 14
Open the brackets
This gives
y = ax² - 18ax + 81a - 14
Set a = 0
So, we have
y = (0)x² - 18(0)x + 81(0) - 14
Evaluate
y = 0x² - 0x - 14
This means that
a = 0
b = 0
c = -14
Add the constants a, b and c
So, we have
Sum of constant = 0 + 0 - 14
Evaluate the sum
Sum of constant = - 14
Hence, the possible value of a + b + c is -14
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Test the series for convergence or divergence. − 2 8 4 9 − 6 10 8 11 − 10 12 identify bn. (assume the series starts at n = 1. )
The given series 2/8 + 4/9 + 6/10 + 8/11 + 10/12 + ..... is a divergent series.
The given series is:
2/8 + 4/9 + 6/10 + 8/11 + 10/12 + .....
Here,
t₁ = 2/8 = (2*1/(1 + 7))
t₂ = 4/9 = (2*2/(2 + 7))
Proceeding in this manner we get the n th term of the given series,
tₙ = (2*n)/(n + 7)
So, now the limit of n th term of the series is given by,
[tex]\lim_{n \to \infty}[/tex] tₙ = [tex]\lim_{n \to \infty}[/tex] (2*n)/(n + 7)) = [tex]\lim_{n \to \infty}[/tex] 2/(1 + 7/n)
Since n tends to infinity
So, 1/n tends to 0. Let 1/n = y
So, 'y' tends to 0.
= [tex]\lim_{y \to 0}[/tex] 2/(1 + 7y) = 2 ≠ 0
Now, difference between (n+1)th and n th term is
= [tex]b_{n+1} - b_n[/tex]
= 2(n+1)/(n +1 +7) - 2n/(n + 7)
= (2(n + 1 + 7) - 14)/(n +1 +7) - (2(n + 7) - 14)/(n + 7)
= 2 - 14/(n + 8) - 2 + 14/(n +7)
= 14/(n +7) - 14/(n +8)
= 14(n + 8 - n - 7)/(n +7)(n +8)
= 14/(n + 7)(n+8) > 0
So, [tex]b_{n+1}\geq b_n[/tex]
Hence the given series diverges.
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According to a research​ survey, 34​%
of adults are pessimistic about the future of marriage and family. That is based on a random sample of about 1900 people from a much larger body of adults. Is it reasonable for research team to use a Normal model for sampling distribution of sample​ proportion?Why or why​ not?
Choose the correct answer below.
A.Yes. The data are from a random​ sample, meeting the Randomization Condition. The data have at least 10 successes and 10​ failures, meeting the​ Success/Failure Condition. The population is much larger than the​ sample, meeting the​ 10% Condition.
B.No. The data are not from a random​ sample, failing the Randomization Condition. The data have at least 10 successes and 10​ failures, meeting the​ Success/Failure Condition. The population is much larger than the​ sample, meeting the​ 10% Condition.
C.Yes. The data are from a random​ sample, meeting the Randomization Condition. The data have less than 10 successes and 10​ failures, meeting the​ Success/Failure Condition. The population is much larger than the​ sample, meeting the​ 10% Condition.
D.No. The data are from a random​ sample, meeting the Randomization Condition. The data have less than 10 successes and 10​ failures, failing the​ Success/Failure Condition. The population is much larger than the​ sample, meeting the​ 10% Condition.
Yes.
The data are from a random sample, meeting the Randomization Condition.
The data have at least 10 successes and 10 failures, meeting the Success/Failure Condition.
The population is much larger than the sample, meeting the 10% Condition. A
It is reasonable for the research team to use a Normal model for the sampling distribution of the sample proportion.
A Normal model for the sampling distribution of a sample proportion, three conditions must be met:
The Randomization Condition, the Success/Failure Condition, and the 10% Condition.
The Randomization Condition is met as the sample is selected randomly from a much larger population of adults.
The Success/Failure Condition is also met because the sample size is large enough (n = 1900) for us to expect at least 10 successes (those who are pessimistic about the future of marriage and family) and 10 failures (those who are optimistic about the future of marriage and family).
The sample proportion of pessimistic adults is 34%, which corresponds to 646 successes in the sample.
The 10% Condition is also met as the sample size (n = 1900) is less than 10% of the total population of adults.
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a rectangle is drawn so the width is 4 inches longer than the height. if the rectangle's diagonal measurement is 56 inches, find the height. give your answer rounded to 1 decimal place
We have the height of the rectangle equal to h = 37.5 inches.
A rectangle is actually about a right triangle. We can use the Pythagorean theorem to generate an expression to find the height of the rectangle.
We know that:
[tex]c^2=a^2+b^2[/tex] so replacing it with the width and length of the rectangle, we get :
[tex]c^2=h^2+w^2[/tex]
We were not given values for the width and length, just their relationship to each other, and we can use that to find an equation in the variable h:
So, [tex]c^2=h^2+w^2[/tex]
[tex](56)^2=h^2+(h+4)^2[/tex]
[tex]3136=h^2+h^2+8h+16[/tex]
[tex]0=2h^2+8h+16-3136[/tex]
[tex]0=2h^2+8h-3,120[/tex]
Since we cannot factor this, we can use the quadratic formula to solve for the height h, where, a = 2 , b = 8, c = -3,120
h = (-b ±[tex]\sqrt{b^2-4ac}[/tex]) /2a
Now, Plug all the values:
h = (-8 ± [tex]\sqrt{8^2-4(2)(-3120)})/4[/tex])
h = -8 ± [tex]\sqrt{64+24,960}/4[/tex]
h =( -8 ± [tex]\sqrt{25,024})/4[/tex]
h = (-8 ± 158.180)/4
There are two possible solutions, so we have:
[tex]h_1=\frac{-8+158.180}{4}[/tex] [tex]h_2=\frac{-8-158.180}{4}[/tex]
[tex]h_1 = 37.545[/tex] [tex]h_2=-41.545[/tex]
[tex]h_1[/tex] ≈ 37.5 in. [tex]h_2[/tex] ≈ -41.5 in.
We cannot use [tex]h_2[/tex] because a negative height is absurd and undefined. Thus, we have the height of the rectangle equal to h = 37.5 inches.
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Write an expression that can be a rule for the number sequence below.
5, 9, 13, 17, 21, …Write an expression that can be a rule for the number sequence below.
5, 9, 13, 17, 21, …
5n, where n is equal to 0, 1, 2, 3, 4
5 + n, where n is equal to 0, 1, 2, 3, 4
5 + 4n, where n is equal to 0, 1, 2, 3
5n + 4, where n is equal to 1, 2, 3, 4
5n, where n is equal to 0, 1, 2, 3, 4
5 + n, where n is equal to 0, 1, 2, 3, 4
5 + 4n, where n is equal to 0, 1, 2, 3
5n + 4, where n is equal to 1, 2, 3, 4
The arithmetic sequence is given by the expression A = 5 + 4n
Given data ,
Let the number sequence be represented as A
Now , the value of A is
A = 5 + 9 + 13 + 17 + 21 ...
On simplifying , we get
The first term of the series is a₁ = 5
Let the second term be a₂ = 9
So , the common difference d = a₂ - a₁
d = 9 - 5 = 4
And , let the number of terms be n
So , the expression is
A = 5 + 4n
when n = 4
A = 5 + 4 ( 4 ) = 25
Hence , the arithmetic sequence is A = 5 + 4n
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Which image has reflectional rotational and point symmetry.
An image that has reflectional, rotational, and point symmetry is a regular polygon. I can explain the terms and help you identify the symmetries in the images.
1. Reflectional symmetry: An image has reflectional symmetry if it can be reflected over a line (called the "line of symmetry") and still look the same as the original image.
2. Rotational symmetry: An image has rotational symmetry if it can be rotated around a point (called the "center of rotation") by a certain angle (less than 360°) and still look the same as the original image.
3. Point symmetry: An image has point symmetry if it looks the same when rotated by 180° around a central point (also called the "point of symmetry").
To determine which image has all three types of symmetry, examine each image and check if it meets the criteria for reflectional, rotational, and point symmetry. Once you identify an image that satisfies all three criteria, you have found the correct image.
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