Answer: Simple random
Step-by-step explanation:
Since , the company randomly selects customers and asks them about their level of satisfaction with the company.
So the chances for each customer to get selected are equal.
This technique of sampling is known as simple random sampling .
Definition:
A simple random sampling is a sampling technique in which the researcher randomly selects individuals from the whole population of interest for his sample.Here , the probability for each individual to get selected is equal as [tex]\dfrac{1}{N}[/tex] , where N = Population size.
In the rest of sampling method (convenience , systematic , stratified and cluster) , the individuals in the population do not have equal chances to get selected. .
The type of sampling used is Cluster Sampling.
Explanation:The type of sampling used in this scenario is Cluster Sampling.
Cluster sampling involves dividing the population into smaller groups or clusters, and then selecting a random sample of clusters to survey.
In this case, the customers are grouped based on their respective clusters in the customer database, and then a random sample of 30 clusters is selected to participate in the satisfaction survey.
A homeowner wants to insulate the new recreation room in her basement. She has been told that 3' of insulation would do the job. The walls are all 9' high and respectively measure 13', 13', 18', and 18' in length. How many rolls will she need if each roll measures 3' x 2' x 50'?
Answer:
6 rolls
Step-by-step explanation:
Data provided in the question:
Height of wall = 9'
Width of walls = 13', 13', 18' and 18'
Dimension of roll = 3' x 2' x 50'
Now,
Total area of the walls = 9' × 13' + 9' × 13' + 9' × 18' + 9' × 18'
= 117 + 117 + 162 + 162
= 558 ft²
Area of each roll = 2' × 50'
= 100 ft²
Thus,
Number of rolls required = [ Total area of the walls ] ÷ [ Area of each roll ]
= 558 ft² ÷ 100 ft²
= 5.58 ≈ 6 rolls
Final answer:
To insulate the recreation room, the homeowner needs to calculate the total area of the walls and then divide it by the area covered by one roll of insulation. After calculating the areas and factoring in the size of the rolls, it is determined that the homeowner needs to purchase 4 rolls of insulation.
Explanation:
The homeowner needs to calculate the amount of insulation needed for a new recreation room. To determine the number of rolls required, we first need to calculate the total area to cover by adding the areas of all four walls. The walls are 9’ high with two of them measuring 13’ in length and the other two are 18’ in length.
The total area These areas can be calculated using the formula Area = Height × Length for each wall. For the 13’ walls: Area = 9’ × 13’ = 117 sq ft (per wall). So, for both, it would be 117 sq ft × 2 = 234 sq ft. And for the 18’ walls: Area = 9’ × 18’ = 162 sq ft (per wall), which is 162 sq ft × 2 = 324 sq ft in total. Now, let's add these together to get the total area of all walls that need insulation: 234 sq ft + 324 sq ft = 558 sq ft.
Next, we calculate how many square feet are in each roll. Since each roll measures 3’ x 50’, the area per roll is 3’ x 50’ = 150 sq ft.
Finally, by dividing the total area needed by the area one roll covers, we can determine the number of rolls:
Number of rolls needed = Total area ÷ Area per roll = 558 sq ft ÷ 150 sq ft/roll ≈ 3.72 rolls.
Since we cannot purchase a fraction of a roll, the homeowner will need to purchase 4 rolls of insulation.
I wish to determine the correlation between the height (in inches) and weight (in pounds) of 21-year-old males. To do this, I measure the height and weight of two 21-year-old men. The measured values are Height and weight of male 1: 70, 169 Height and weight of male 2: 69,164 The correlation r computed from the measurements on these males is Question 2 options: 1.0 -1.0 near 0 because the heights and weights of the men are similar.
Answer:
[tex]r=\frac{2(23146)-(139)(333)}{\sqrt{[2(9661) -(139)^2][2(55457) -(333)^2]}}=1[/tex]
So then the we have perfect linear association. Because the heights and weights of the men are similar.
Step-by-step explanation:
Let X represent the Height and Y the weigth
We have the follwoing dataset:
X: 70, 69
Y: 169, 164
n=2
The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.
And in order to calculate the correlation coefficient we can use this formula:
[tex]r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}[/tex]
For our case we have this:
n=2 [tex] \sum x = 139, \sum y = 333, \sum xy = 23146, \sum x^2 =9661, \sum y^2 =55457[/tex]
And if we replace in the formula we got:
[tex]r=\frac{2(23146)-(139)(333)}{\sqrt{[2(9661) -(139)^2][2(55457) -(333)^2]}}=1[/tex]
So then the we have perfect linear association. Because the heights and weights of the men are similar.
Find the standard deviation of the following data. Answers are rounded to the nearest tenth. 5, 5, 6, 12, 13, 26, 37, 49, 51, 56, 56, 84
Answer:
24.2(to the nearest tenth)
Step-by-step explanation:
The question is ungrouped data type
standard deviation =√ [∑ (x-μ)² / n]
mean (μ)=∑x/n
= [tex]\frac{5+5+6+12+13+26+37+49+51+56+56+84}{12}[/tex]
=33.3
x-μ for data 5, 5, 6, 12, 13, 26, 37, 49, 51, 56, 56, 84 will be
-28.3, -28.3, -27.3, -21.3, -7.3, 3.7, 15.7,17.7, 22.7,22.7,50.7
(x-μ)² will be 800.89, 800.89,745.29,453.69,53.29,13.69,246.49,313.29,515.29,515.29,2570.49
∑ (x-μ)² will be = 7028.59
standard deviation = √(7028.59 / 12)
=24.2
Company A offers a $35,000 annual salary plus a 6% commission of his total sales. Company B offers a flat annual salary of $36,000.How much would you need to have in total sales to earn the same amount in each job?
Answer: you need to have in total sales of $16667 to earn the same amount in each job
Step-by-step explanation:
Let x represent the amount that you need to have in total sales in order to earn the same amount in each job.
Company A offers a $35,000 annual salary plus a 6% commission of his total sales. This means that the total amount earned with company A when x sales is made yearly would be
35000 + 0.06x
Company B offers a flat annual salary of $36,000. This means that the total amount earned with company B yearly would be
36000
To earn the same amount with both jobs,
35000 + 0.06x = 36000
0.06x = 36000 - 35000
0.06x = 1000
x = 1000/0.06 = $16667
In the test of gender selection technique, results consisted of 281 baby girls and 291 baby boys. Based on this result, what is the probability of a girl born to a couple using this technique? Does it appear that the technique is effective in increasing the likelihood that a baby will be a girl?
-The probability that a girl will be born using this technique is approximately______
Does this technique appear effective in improving the likelihood of having a baby girl?
Answer:
The probability for a girl to be born is 0.4913. This technique doesnt appear to improve the likelihood of having a baby girl.
Step-by-step explanation:
Since the number of babies selected for this technique, using the law of big numbers, we conclude that the proportion of babies that are girls in the selection is approximately equal than the probability for a girl to be selected. Thus, the probability that a girl will be born using the technique is 281/(281+291) = 0.4913.
Since in general girls are slightly more likely to be born than boys, then we can conclude that the technique doesnt have an effect in improving the likelihood of having a baby girl, but the opposite.
The side of a cube is 9 cm long.What is the cube's surface area? ____ cm2A) 27B) 729 C) 486What is the cube's volume?Lol 729 ____ cm3A) 27B) 729C) 486
Answer:C, B
Step-by-step explanation:
Warning! No identities used in the lesson may be submitted. Create your own using the columns below. See what happens when different binomials or trinomials are combined. Square one factor from column A and add it to one factor from column B to develop your own identity. Column A (x - y) (x + y) (y + x) (y - x) Column B (x2 + 2xy + y2) (x2 - 2xy + y2) (ax + b) (cy + d)
The question is asking to create a new mathematical identity by combining binomials and trinomials from two different columns. An example of such identity could be 2x2 + 2y2. We also used the appendix to solve a quadratic equation by completing the square.
Explanation:This question is asking you to combine binomials and trinomials from column A and column B to create a new mathematical identity. An example of creating such an identity could be squaring the binomial (x - y) from column A and adding it to the trinomial (x2 + 2xy + y2) from column B.
So, if we square (x - y), we get x2 - 2xy + y2. Adding that to x2 + 2xy + y2 from column B, we get 2x2 + 2y2, which is the new identity.
Also, using the appendix to solve an equation of the form ax² + bx + c = 0, we rearrange terms and complete the square to find x. Using the example of x² +0.0211x -0.0211 = 0, the factors of 0.0211 are easy to determine. After rearranging terms, the equation becomes (x +0.01055)² - 0.0211 = 0. Finally, to solve for x, you would add 0.0211 to both sides and then take a square root.
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A school marching band will raise one dollar for each granola bar and five dollars for each pie they sell. Yesterday, they raise $260 by selling 80 bars and pies. How many of each did they sell?
Answer: 35 granola bars and 45 pies were sold.
Step-by-step explanation:
Let x represent the number of granola bar that was sold.
Let y represent the number of pie that was sold.
A school marching band will raise one dollar for each granola bar and five dollars for each pie they sell. Yesterday, they raise $260 by selling 80 bars and pies.
This means that
x + 5y = 260 - - - - - - - - - -1
Since they sold a total of 80 bars and pies, it means that
x + y = 80
Substituting x = 80 - y into equation 1, it becomes
80 - y + 5y = 260
- y + 5y = 260 - 80
4y = 180
y = 180/4 = 45
x = 80 - y = 80 - 45
x = 35
Weinstein, McDermott, and Roediger (2010) con- ducted an experiment to evaluate the effectiveness of different study strategies. One part of the study asked students to prepare for a test by reading a passage. In one condition, students generated and answered questions after reading the passage. In a se tion, students simply read the passage a second time. All students were then given a test on the passage material and the researchers recorded the number of correct answers.
a. Identify the dependent variable for this study.
b. Is the dependent variable discrete or continuous?
c. What scale of measurement (nominal, ordinal, interval, or ratio) is used to measure the dependent variable?
Answer:
a) The number of correct answers
b) Discrete
c) Ratio
Step-by-step explanation:
We are given the following in the question:
Experiment:
Evaluate the effectiveness of different study strategies. All students were then given a test on the passage material and the researchers recorded the number of correct answers.
a) The dependent Variable
The number of correct answers given is the dependent variable because it depends on the number of times the passage is read.
b) Nature of dependent variable.
It is a discrete variable.Since, the number of questions will always be expressed in whole numbers and cannot be expressed as decimals. They are always counted and not measured.c) Scale of measurement
Ratio is used to measure the dependent variable because true zero for the number of correct questions answered exist.If the measure is zero that means truly no questions were answered correctly.The correct answers are as follows: a: number of correct answers on the test, b: discrete, and c: ratio scale.
a. The dependent variable for this study is the number of correct answers on the test.
b. The dependent variable is discrete because it consists of countable values, specifically the number of questions answered correctly, which can only be whole numbers.
c. The scale of measurement used to measure the dependent variable is the ratio scale. This is because the number of correct answers has a true zero point (it is possible to have zero correct answers), and the differences between the numbers of correct answers are meaningful and consistent. Additionally, the ratio scale allows for the comparison of ratios, such as one student answering twice as many questions correctly as another.
To elaborate, in experimental design, the dependent variable is the variable that is measured to assess the effect of the independent variable (in this case, the study strategy). The dependent variable is what changes as a result of manipulating the independent variable. In this study, the researchers are interested in how different study strategies affect test performance, so they measure test performance by counting the number of correct answers each student provides.
The nature of the dependent variable as discrete or continuous depends on whether the data can take on any value within a range (continuous) or only specific values (discrete). Since the number of correct answers can only be whole numbers (e.g., 5 correct answers, not 5.5), it is discrete.
Finally, the scale of measurement indicates the level of precision with which the variable is measured. The nominal scale is used for categorical data without any order (e.g., gender, race). The ordinal scale is used for data that can be ranked but without equal intervals between ranks (e.g., socioeconomic status). The interval scale is used for data with equal intervals between values but no true zero (e.g., temperature in Celsius or Fahrenheit). The ratio scale is used for data with a true zero and equal intervals between values, allowing for the comparison of ratios (e.g., height, weight, and in this case, the number of correct answers). Since the number of correct answers can be zero (indicating no correct answers) and the differences between scores are meaningful, the dependent variable in this study is measured on a ratio scale.
If 9\geq4x+19≥4x+19, is greater than or equal to, 4, x, plus, 1, which inequality represents the possible range of values of 12x+312x+312, x, plus, 3?
Answer:
[tex]12x+3\leq 27[/tex]
Step-by-step explanation:
It is given that
[tex]9\geq4x+1[/tex]
We need to find the possible range of values of 12x+3.
Subtract -1 from both sides.
[tex]9-1\geq 4x[/tex]
[tex]8\geq 4x[/tex]
Multiply both sides by 3.
[tex]24\geq 12x[/tex]
Add 3 on both sides.
[tex]24+3\geq 12x+3[/tex]
[tex]27\geq 12x+3[/tex]
It can be rewritten as
[tex]12x+3\leq 27[/tex]
Therefore, 12x+3 must be less than or equal to 27.
A quadrilateral has no pairs of parallel sides. Which name best describes the figure?
rectangle
trapezoid
parallelogram
kite
Answer:
Therefore,
A quadrilateral that has no pairs of parallel sides is
KITE.
Step-by-step explanation:
A quadrilateral that has no pairs of parallel sides is
KITE.
In Kite there are no pairs of Parallel sides.
The Figure for Kite ABCD is below (not to the scale).
Rectangle and Parallelogram:
Opposite sides are Parallel .
Hence they have pairs of parallel sides,
Trapezoid:
Trapezoid has one pair of parallel side.
Hence it has a pair of parallel sides,
Therefore,
A quadrilateral that has no pairs of parallel sides is
KITE.
Answer:
Kite
Step-by-step explanation:
In a set of normally distributed test scores that have a mean of 100 and standard deviation of 15, it would be correct to conclude that approximately 68 percent of the scores would fall between _____ and _____.
Answer:
It would be correct to conclude that approximately 68 percent of the scores would fall between 85 and 115.
Step-by-step explanation:
We are given the following in the question:
Mean, μ = 100
Standard Deviation, σ = 15
We are given that the distribution is a bell shaped distribution that is a normal distribution.
Empirical rule
Also known as 68-95-99.7 rule.It states that almost all data lies within three standard deviation of mean for a normal distribution.About 68% of data lies within one standard deviation of mean.About 95% of data lies within two standard deviation of mean.About 99.7% of data lies within three standard deviation of mean.Thus, approximately 68% of data will lie within one standard deviation of mean.
[tex]\mu - \sigma = 100-15 = 85\\\mu + \sigma = 100 + 15 = 115[/tex]
Thus, it would be correct to conclude that approximately 68 percent of the scores would fall between 85 and 115.
68 percent of the scores would fall between 85 and 115.
Empirical ruleEmpirical rule states that for a normal distribution, about 68% are within one standard deviation from the mean, 95% are within two standard deviation from the mean and 99.7% are within three standard deviation from the mean.
Given that mean(μ) = 100 and standard deviation (σ) = 15
68 percent of the scores would fall between μ ± σ = 100 ± 15 = 85, 115
68 percent of the scores would fall between 85 and 115.
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(1) 4m+5=3m-5/2 (2) -2+7(x+2)=5(2x-2)+4 Show work for every step.
Answer:
m = -3x = 6Step-by-step explanation:
1)
[tex]4m+5=\dfrac{3m-5}{2} \quad\text{given}\\\\2(4m+5)=\dfrac{2(3m-5)}{2} \quad\text{multiply by 2}\\\\8m+10=3m-5 \quad\text{use the distributive property}\\\\(8m+10)-(3m+10)=(3m-5)-(3m+10) \quad\text{subtract $3m+10$}\\\\5m=-15 \quad\text{collect terms}\\\\\dfrac{5m}{5}=\dfrac{-15}{5} \quad\text{divide by 5}\\\\m=-3 \quad\text{simplify}[/tex]
____
2)
[tex]-2+7(x+2)=5(2x-2)+4 \quad\text{given}\\\\-2+7x+14=10x-10+4 \quad\text{use the distributive property}\\\\7x+12=10x-6 \quad\text{collect terms}\\\\(7x+12)-(7x-6)=(10x-6)-(7x-6) \quad\text{subtract $7x-6$}\\\\18=3x \quad\text{collect terms}\\\\\dfrac{18}{3}=\dfrac{3x}{3} \quad\text{divide by 3}\\\\6=x \quad\text{simplify}[/tex]
the area of a circle is less than 64 π. which of the following can be the circumference of the circle? (select one or more answer choices)
a. 12 π
b. 16 π
c. 24 π
d. 32 π
Answer:
d. 32 π
Step-by-step explanation:
As given
Area of circle = 64 π
Area of circumference = 1/2*(Area of circle)
Area of circumference = 1/2*(64π)
Area of circumference = 0.5*64π
Area of circumference = 32π
A circle is a curve sketched out by a point moving in a plane. The correct option is A, 12π unit.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.
Given that the area of the circle is less than 64π. Therefor, the area of the circle can be written as,
Area of the circle < 64π units²
πR² < 64π
R < 8 units
Now, the circumference of the circle should be less than the circumference of the circle having radius of 8 units. Therefore, we can write,
Circumference of the circle with radius R < Circumference of the circle with radius of 8 units
2πR < 2 × π × 8 units
2πR < 16π units
Therefore, from the above inequality the circumference of the circle should be less than 16π unit. Since the only feasible option is 12π.
Hence, the correct option is A, 12π unit.
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Identify the sample chosen for the study.
The number of times 13 out of 22 students on your floor order take-out in a week.
All students who order take-out in a week. The 13 students on your floor. The 22 students on your floor.
Answer:
The 13 students on floor
Step-by-step explanation:
The sample is a portion of population selected to view the aspects of population as whole population is difficult to follow. Here, the sample is 13 students on the floor because it is selected from 22 students on the floor.
The population consists of 22 students on floor and 13 out of 20 is the sample because it is a portion of population.
A binomial event has n = 50 trials. The probability of success for each trial is 0.60. Let x be the number of successes of the event during the 50 trials. What are μx and σx?
30 and 3.4641
30 and 5.4772
20 and 3.4641
20 and 5.4772
50 and 3.4641
Answer:
A. 30 and 3.4641
Step-by-step explanation:
The solution is Option A.
The value of the standard deviation is given by μx = 30 and σx = 3.4641
What is Standard Error?The standard deviation of a statistic's sample distribution, or an approximation of that standard deviation, is the statistic's standard error. The standard error of the mean is used when referring to a statistic that is the sample mean. The standard error of the mean, or simply standard error, indicates how different the population mean is likely to be from a sample mean.
The standard error S = √ [ ( 1 - p ) p / n ]
where p = population proportion
n = sample size
Given data ,
Let the number of trials n = 50
Let the probability of success be represented as p = 0.60
Now , let the standard deviation be σ
S = √ [ ( 1 - p ) p / n ]
Substituting the values in the equation , we get
S = √ ( 0.60 ) ( 0.40 ) / 50
S = √ 0.24/50
S = √0.0048
S = 0.0692820
So , the value of σ = 0.0692820
Therefore , the value of σx = 0.0692820 x 50 = 3.4641
Now , the value of μx = 0.60 x 50 = 30
Hence , the value of μx and σx are 30 and 3.4641 respectively
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Trevor stores his baseball cards in a book with nine pages each page holds nine cards seven of his cards won't fit in the book how many cards does he have
Answer:
88
Step-by-step explanation:
9 pages
Each holds 9
He has 7 more
81+7=88
what is the midpoint of a line segment with the endpoints (8, -3) and (-5, -9)?
A (2.5, -7)
B (1.5, -6)
C (-7, 2.5)
D (-6, 1.5)
Answer:
The answer to your question is B. (1.5, -6)
Step-by-step explanation:
Data
A (8, -3)
B (-5, -9)
Formula
Xm = [tex]\frac{x1 + x2}{2}[/tex]
Ym = [tex]\frac{y1 + y2}{2}[/tex]
Substitution
x1 = 8 x2 = -5
Xm = [tex]\frac{8 - 5}{2} = \frac{3}{2}[/tex]
y1 = -3 y2 = -9
Ym = [tex]\frac{-3 - 9}{2} = \frac{-12}{2} = -6[/tex]
Midpoint = (3/2, -6) = (1.5, -6)
The amount of simple interest earned I, on an investment over a fixed amount of time ????, is jointly proportional to the principle invested P, and the interest rate ????. A principle investment of $1500.00 with an interest rate of 5% earned $375.00 in simple interest. Find the amount of simple interest earned if the principle is $2300.00 and the interest rate is 8%?
Answer:$920
Step-by-step explanation:
Since the variation is joint, I=KPr where k is the constant of proportionality.
Plugging in the values of I=$375, P=$1500 and r=5% in the equation I=KPr, the value of k can be calculated. Hence, the formula connecting the three quantities (I,P and r) can be generated.
375 = K (1500×5)
Making k the subject of change,
K = 375/(1500×5)
K=1/20
Formula connecting the three quantities :I =Pr/20
when P=$2300, r=8%,
I = (2300×8)/20
I = $920
Cluster sampling is _____. A. a probability sampling methodB. a nonprobability sampling methodC. the same as convenience samplingD. None of these answers are correct
Answer:
A.
Step-by-step explanation:
Probability sampling means that each unit in population has an equal chance or probability of selection in a sample.
Cluster sampling is a probability sampling method because population is divided into clusters at random and no personal judgement is involved. Thus, each cluster has equal probability of selecting and sampling is done as random. Hence, cluster sampling is a probability sampling method.
Cluster sampling is a probability sampling method. Here option A is correct.
It involves dividing the population into clusters or groups based on certain characteristics, such as geographical location or other relevant attributes. Then, a random sample of clusters is chosen, and all individuals within those selected clusters become part of the sample.
This method is considered probabilistic because each cluster has a known probability of being selected, and thus each individual within the chosen clusters has a chance of being included in the sample. This makes it possible to estimate population parameters and make statistical inferences.
Cluster sampling differs from other probability sampling methods, such as simple random sampling, in that it involves a multi-stage process.
It is particularly useful when it's impractical or too costly to gather a complete list of all individuals in the population, making it a valuable tool in various fields of research, including public health, sociology, and economics. Here option A is correct.
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In a recent year, Washington State public school students taking a mathematics assessment test had a mean score of 276.1 and a standard deviation of 34.4. A random sample of 64 students is drawn form this population.(A) Identifying the mean and standard error of the sample mean score ¯X (x bar).(B) What is the distribution of ¯ X? and Why?(C) Find the probability that the sample mean score ¯X(x bar) is at least 285.
Answer:
a) [tex] \mu_{\bar x} =\mu = 276.1[/tex]
[tex]\sigma_{\bar x} =\frac{\sigma}{\sqrt{n}}=\frac{34.4}{\sqrt{64}}=4.3[/tex]
b) From the central limit theorem we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:
[tex]\bar X \sim N(\mu=276.1, \frac{\sigma}{\sqrt{n}}=4.3)[/tex]
c) [tex]P(\bar X \geq 285)=P(Z\geq \frac{285-276.1}{4.3}=2.070)[/tex]
[tex]P(Z\geq2.070)=1-P(Z<2.070)=1-0.981=0.019[/tex]
Step-by-step explanation:
Let X the random variable the represent the scores for the test analyzed. We know that:
[tex] \mu=E(X) = 276.1 , \sigma=Sd(X) = 34.4[/tex]
And we select a sample size of 64.
The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".
Part a
For this case the mean and standard error for the sample mean would be given by:
[tex] \mu_{\bar x} =\mu = 276.1[/tex]
[tex]\sigma_{\bar x} =\frac{\sigma}{\sqrt{n}}=\frac{34.4}{\sqrt{64}}=4.3[/tex]
Part b
From the central limit theorem we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:
[tex]\bar X \sim N(\mu=276.1, \frac{\sigma}{\sqrt{n}}=4.3)[/tex]
Part c
For this case we want this probability:
[tex] P(\bar X \geq 285)[/tex]
And we can use the z score defined as:
[tex] z=\frac{\bar x -\mu}{\sigma_{\bar x}}[/tex]
And using this we got:
[tex]P(\bar X \geq 285)=P(Z\geq \frac{285-276.1}{4.3}=2.070)[/tex]
And using a calculator, excel or the normal standard table we have that:
[tex]P(Z\geq2.070)=1-P(Z<2.070)=1-0.981=0.019[/tex]
The radius of a spherical balloon being filled with air expands at 4 cm^3 per minute. Assuming the balloon fills in spherical shape, how fast is the radius of the spherical balloon increasing in cm per minute after 2.25 minutes?
Answer: dr/dt = 0.042 cm/minute
Step-by-step explanation:
Given;
dV/dt = 4cm^3/minute
t = 2.25minutes
Volume of a sphere is given as;
V = (4/3)πr^3
Change in Volume ∆V can be derived by differentiating the function.
dV/dt= 4πr^2 . dr/dt
dV/dt = 4πr^2dr/dt ....1
dV/dt is given as 4 cm^3/min
radius after 2.25 minutes can be gotten from the the volume.
Volume after 2.25mins = 4×2.25 = 9cm^3
9cm^3 = V = 4/3πr^3
r^3 = 27/4π
r = (27/4π)^1/3
From equation 1.
dr/dt = (dV/dt)/4πr^2 = 4/(4πr^2) = 1/(πr^2)
dr/dt = 1/(π(27/4π)^2/3)
dr/dt = 0.042cm/minute.
Megan spent two out of five of her money on a doll and half of the remainder on a musical box she spent eight dollars more on the doll than on a musical box how much money did she have left
Answer:
Megan has left with $24.
Step-by-step explanation:
Let the total money she has be 'y'.
Given:
Megan spent two out of five of her money on a doll.
So we can say that;
Money spent on doll = [tex]\frac{2}{5}y[/tex]
Also Given:
half of the remainder on a musical box.
Money spent on musical box = [tex](y-\frac{2}{5}y)\frac{1}2[/tex]
Now we will make the denominator common using LCM we get;
Money spent on musical box =[tex](\frac{5y}{5}-\frac{2y}{5})\times\frac{1}2}=(\frac{5y-2y}{5})\times \frac{1}{2}=\frac{3y}{10}[/tex]
Now Given:
she spent eight dollars more on the doll than on a musical box.
[tex]\frac{2y}{5} = \frac{3y}{10}+8[/tex]
Combining like terms we get;
[tex]\frac{2y}{5}-\frac{3y}{10}=8[/tex]
Now we will make the denominator common using LCM we get;
[tex]\frac{2y\times2}{5\times2}-\frac{3y}{10}=8\\\\\frac{4y}{10}-\frac{3y}{10}=8\\\\\frac{4y-3y}{10}=8\\\\y=8\times10\\\\y=\$80[/tex]
Money spent on doll = [tex]\frac{2}{5}y=\frac{2}{5}\times 80 = \$32[/tex]
she spent eight dollars more on the doll than on a musical box.
So we can say that;
Money spent on musical box = Money spent on doll -8 = [tex]32-8 = \$24[/tex]
Now to find the remaining money left we will subtract Money spent on doll and Money spent on musical box from total money she had.
framing in equation form we get;
remaining money left = [tex]80-32-24= \$24[/tex]
Hence Megan has left with $24.
What was the importance of the massacre of 270 Indians by U.S. military forces at Sand Creek, Colorado, in 1864?
Answer:
That the government did not defend the rights of the Indians.
Step-by-step explanation:
Sand Creek, Colorado was the place where hundreds of Cheyenes and Arapahoes were massacred by the Colorado Territory militia, which terrorized indigenous peoples to abandon their lands.
help fast pleaese Given a pyramid l = w = 9.0 mm and V = 324.0 cubic mm , find h in mm.
(Enter a numerical answer)
Answer: h = 12mm
Step-by-step explanation:
The volume of a pyramid is given as :
V = [tex]\frac{1}{3}[/tex] lwh
Therefore:
324 = [tex]\frac{1}{3}[/tex] lwh
324 x 3 = 9 x 9 x h
Therefore:
h = 972/81
h = 12mm
P(x)=2x^4-x^3+2x^2-6. What is the remainder when P(x) is divided by (x-2)?
Answer: 26
Step-by-step explanation: From the remainder theorem ,
If P (x) = 2x⁴ ⁻ x³ + 2x² ⁻ 6. is divided by ( x - 2 ).
It means that if P(x) is divided by (x - 2 ) and leaves a Remainder, it implies that x - 2 is not a factor of P(x) , but if it leaves no remainder, it means x-2 is a factor of P(x).
Therefore , to find the remainder, find the zero of x - 2, and substitutes for the value in P(x) to know the remainder
x - 2 = 0
x = 2
Now put this in P(x)
P(x) = 2(2)⁴ - (2)³ + 2(2)² - 6
= 2(16) -8 + 2(4) -6
= 32 -8 +8 -6
=26
Therefore the remainder when P(x) is divided by x -2
=26
Note: Since the division of P(x) by x - 2 leaves a remainder, it means that
x - 2 ≠ a factor of P(x)
If z varies jointly with x and y, x = 2 and y = 2, z = 7. Find z when x = 4 and y = 8.
Answer:
56
Step-by-step explanation:
z varies jointly with x and y:
z = kxy
When x = 2 and y = 2, z = 7.
7 = k(2)(2)
k = 7/4
z = 7/4 xy
When x = 4 and y = 8:
z = 7/4 (4)(8)
z = 56
A broker takes 2% as commission for the sale of property of value up to rupees 3,00,000. If the sale price is more than this, the broker changes 1.5% for the remaining amount. If a property was sold for rupees 4,50,000.What was the broker's commission.
Answer:
The broker's commission was rupees 8,250
Step-by-step explanation:
Selling price of property = rupees 450,000
The sale price is higher than rupees 300,000
Commission for rupees 300,000 = 2% × rupees 300,000 = rupees 6,000
Remaining amount = rupees 450,000 - rupees 300,000 = rupees 150,000
Commission for the remaining amount = 1.5% × rupees 150,000 = 0.015 × rupees 150,000 = rupees 2,250
Total commission = rupees 6,000 + rupees 2,250 = rupees 8,250
What is the percent increase between getting a high school scholarship and bachelors degree when high school scholarship is $421 and bachelors degree is $670
Answer:
The percent increase between getting a high school scholarship and bachelor's degree is 59.14%.
Step-by-step explanation:
Given:
High school scholarship is $421.
Bachelor's degree is $670.
Now, to find the percent increase between a high school scholarship and bachelor's degree.
So, we get the amount of increase between a high school scholarship and bachelor's degree.
[tex]670-421=249.[/tex]
Thus, the amount of increase = $249.
Now, to get the percent increase between a high school scholarship and bachelor's degree:
[tex]\frac{249}{421}\times 100[/tex]
[tex]=\frac{24900}{421}[/tex]
[tex]=59.14\%.[/tex]
Therefore, the percent increase between getting a high school scholarship and bachelor's degree is 59.14%.
The percent increase from a high school scholarship ($421) to a bachelor's degree ($670) is calculated to be roughly 59.1%. The overall value of a bachelor's degree over a lifetime typically exceeds this amount, with degree holders potentially earning millions more than their counterparts with only a high school diploma.
Explanation:The subject of this question is a mathematical one, dealing with percentage increase. To find the percent increase between getting a high school scholarship and a bachelor's degree, we first subtract the smaller value (high school scholarship) from the larger value (bachelor's degree). We then divide the result by the starting value (high school scholarship). Thus, the formula is: [(670 - 421)/421] * 100%.
A simplified calculation gives us: [(249)/421] * 100% = 59.1%.
Therefore, there is a 59.1% increase in the value from a high school scholarship to a bachelor's degree based on the given figures.
It's also worth noting that over the course of a career, according to a 2021 report from the Georgetown University Center on Education and the Workforce, adults with a bachelor's degree earn an average of $2.8 million during their careers, $1.2 million more than the median for workers with a high school diploma.
Learn more about Percent Increase here:https://brainly.com/question/18960118
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Which statement is correct using "is not equal to'' (≠)? A) 70 pieces of candy divided equally between 5 friends _____ 14 pieces each. B) 95 pieces of candy divided equally between 5 friends _____ 19 pieces each. C) 115 pieces of candy divided equally between 5 friends _____ 21 pieces each. D) 145 pieces of candy divided equally between 5 friends _____ 29 pieces each. Eliminate
Answer: C. 115 pieces of candies divided equally between 5 friends is not equal to 21 each
Step-by-step explanation: 115 divided by 5 is 23 each and not 21.