Using the formula for a 95% confidence interval and a Z score of 1.96, Joseph's 95% confidence interval for the percentage of students reporting bullying at their school is roughly 10.1% to 11.9%.
Explanation:The subject of this problem is statistics, specifically the creation of a 95% confidence interval based on collected data. A confidence interval is a type of estimate computed from the statistics of observed data. This gives a range of values for an unknown parameter (in this case, the number of students experiencing bullying).
In this case, the mean (or average) is 0.15 or 15%. The standard deviation is 0.045 or 4.5%. The sample size, often denoted as 'n', is 186.
Based on the 95% confidence interval, we will use a Z score of 1.96. We can start to calculate our interval using the formula for the confidence interval: sample mean ± (Z * (standard deviation/sqrt(n))).
Using these numbers:
The lower end of the confidence interval is 0.11 - (1.96 * (0.045 / sqrt(186))) = about 0.101 or 10.1%.
The upper end of the confidence interval is 0.11 + (1.96 * (0.045 / sqrt(186))) = about 0.119 or 11.9%.
So, the 95% confidence interval for the percentage of students who reported experiencing bullying one to three times within the most recent month is approximately 10.1% to 11.9%.
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A publisher reports that 47%47% of their readers own a personal computer. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 280280 found that 43%43% of the readers owned a personal computer. Make the decision to reject or fail to reject the null hypothesis at the 0.010.01 level.
Answer:
The null hypothesis was not rejected.
The proportion of readers who own a personal computer is 47%.
Step-by-step explanation:
The claim made by a publisher is that 47% of their readers own a personal computer.
A single proportion z-test can be used to determine whether the claim made by the publisher is authentic or not.
The hypothesis for this test can be defined as follows:
H₀: The proportion of readers who own a personal computer is 47%, i.e. p = 0.47.
Hₐ: The proportion of readers who own a personal computer is different from 47%, i.e. p ≠ 0.47.
The information provided is:
[tex]n=280\\\hat p=0.43\\\alpha =0.01[/tex]
The test statistic is:
[tex]z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}=\frac{0.43-0.47}{\sqrt{\frac{0.47(1-0.47)}{280}}}=-1.34[/tex]
The test statistic value is, z = -1.34.
Decision rule:
If the p-value of the test is less than the significance level α = 0.01 then the null hypothesis will be rejected and vice-versa.
Compute the p-value as follows:
[tex]p-value=2\times P (Z < z)[/tex]
[tex]=2\times P (Z < -1.34)\\=2\times [1-P(Z<1.34)]\\=2\times [1-0.90988]\\=0.18024\\\approx0.18[/tex]
*Use a z table for the probability.
The p-value of the test is 0.18.
p-value = 0.18 > α = 0.01
The null hypothesis was failed to be rejected at 1% level of significance.
Conclusion:
There is enough evidence to support the claim made by the publisher. Hence, it can be concluded that the proportion of readers who own a personal computer is 47%.
There are 327 official ports of entry in the United States. The Department of Homeland Security selects 15 ports of entry at random to be audited for compliance with screening procedures of incoming travelers through the primary and secondary vehicle and pedestrian lanes. What kind of sample is this (simple random, systematic, stratified, cluster)?
Answer:
RANDOM
Step-by-step explanation:
A sailboat is sitting at rest near its dock. A rope attached to the bow of the boat is drawn in over a pulley that stands on a post on the end of the dock that is 5 feet higher than the bow. If the rope is being pulled in at a rate of 2 feet per second, how fast is the boat approaching the dock when the length of rope from bow to pulley is 13 feet
Answer:
The boat is approaching the dock at rate of 2.14 ft/s
Step-by-step explanation:
The situation given in the question can be modeled as a triangle, please refer to the attached diagram.
A rope attached to the bow of the boat is drawn in over a pulley that stands on a post on the end of the dock that is 5 feet higher than the bow that means x = 5 ft.
The length of rope from bow to pulley is 13 feet that means y = 13 ft.
We know that Pythagorean theorem is given by
[tex]x^{2} + y^{2} = z^{2}[/tex]
Differentiating the above equation with respect to time yields,
[tex]2x\frac{dx}{dt} + 2y\frac{dy}{dt} = 2z\frac{dz}{dt}[/tex]
[tex]x\frac{dx}{dt} + y\frac{dy}{dt} = z\frac{dz}{dt}[/tex]
dx/dt = 0 since dock height doesn't change
[tex]y\frac{dy}{dt} = z\frac{dz}{dt}[/tex]
[tex]\frac{dy}{dt} = \frac{z}{y} \frac{dz}{dt}[/tex]
The rope is being pulled in at a rate of 2 feet per second that is dz/dt = 2 ft/s
First we need to find z
z² = (5)² + (13)²
z² = 194
z = √194
z = 13.93 ft
So,
[tex]\frac{dy}{dt} = \frac{z}{y} \frac{dz}{dt}[/tex]
[tex]\frac{dy}{dt} = \frac{13.93}{13}(2)[/tex]
[tex]\frac{dy}{dt} = 2.14[/tex] [tex]ft/s[/tex]
Therefore, the boat is approaching the dock at rate of 2.14 ft/s
So, the boat approached the dock with a speed of 2.1337 m/sec.
Pythagoras Theorem:Pythagoras Theorem is an important topic in Maths, which explains the relation between the sides of a right-angled triangle.
So, the formula is,
[tex]a^2+b^2=c^2[/tex]
Differentiating the above equation,
[tex]2a\frac{da}{dt} +2b\frac{db}{dt} =2c\frac{dc}{dt} ...(1)[/tex]
It is given that,
[tex]a=5m\\\frac{da}{dt}=0\\ c=13\\\frac{dc}{dt}=2 m/s[/tex]
[tex]b=\sqrt{13^2-5^2} \\b=12 m/s[/tex]
Substituting the above values in equation (1) we get,
[tex]2\times5\times0+2\times12\frac{db}{dt} =2\times13\times2\\\frac{db}{dt} =\frac{26}{12}\\ \frac{db}{dt} =2.1337 m/s[/tex]
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For students who first enrolled in two year public institutions in a recentsemester, the proportion who earned a bachelor's degree within six years was 0.398 The president of a certain college believes that the proportion of students who enroll in her institution have a higher completion rate.
(A) Determine the null and alternative hypotheses.
(B) Explain what it would mean to make a Type I error.
(C) Explain what it would mean to make a Type II error.
Answer:
A) Null hypothesis: H0: p = 0.398
Alternative hypothesis: H0: p < 0.398
B) A type I error would be made if the president concludes that he rejects the null hypothesis even when it's true.
C) A type II error would be made if the president concludes that the null hypothesis is false, but he erroneously fails to reject it.
Step-by-step explanation:
A) The null and alternative hypotheses are given below:
From the given information, the claim is that the proportion of students who enroll in her institution have a lower completion rate. This is representing the alternative hypothesis. Thus
Null hypothesis:
H0: p = 0.398
Alternative hypothesis:
H0: p < 0.398
B) A type I error would be made if the president concludes that he rejects the null hypothesis even when it's true.
C) A type II error would be made if the president concludes that the null hypothesis is false, but he erroneously fails to reject it.
-7y = -91, what is the value of y
Answer: The value of y is 13
Step-by-step explanation: To find the value of y, we will use properties of equality.
Step 1: -7y = -91 (We want to find the value of y, or 1 y)
Step 2: (Use the division property of equality) -7y/-7 = -91/-7
Step 3: (Answer) y = 13
Answer:
y= 13
Step-by-step explanation:
-7y = -91
divide both sides by -7
y = 13
Suppose that an accounting firm does a study to determine the time needed to complete one person's tax forms. It randomly surveys 175 people. The sample mean is 22.8 hours. There is a known population standard deviation of 6.4 hours. The population distribution is assumed to be normal. NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)
Construct a 90% confidence interval for the population mean time to complete the tax forms.
i. State the confidence interval. (Round your answers to two decimal places.)
ii. Calculate the error bound. (Round your answer to two decimal places.
Answer:
Step-by-step explanation:
Considering the central limit theorem, the distribution is normal since the number of samples is large. Also, the population standard
deviation is known. We would determine the z score.
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.90 = 0.1
α/2 = 0.1/2 = 0.05
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.05 = 0.95
The z score corresponding to the area on the z table is 2.05. Thus, confidence level of 90% is 1.645
Confidence interval is written in the form,
(Sample mean - margin of error, sample mean + margin of error)
The sample mean, x is the point estimate for the population mean.
Confidence interval = mean ± z × σ/√n
Where
σ = population standard Deviation
Confidence interval = x ± z × σ/√n
x = 22.8 hours
σ = 6.4 hours
n = 175
i) Confidence interval = 22.8 ± 1.645 × 6.4/√175
= 22.8 ± 0.80
The lower end of the confidence interval is
22.8 - 0.80 = 22
The upper end of the confidence interval is
22.8 + 0.80 = 23.6
ii) error bound is the same as the margin of error
Error bound = 0.8
Suppose that a company wishes to predict sales volume based on the amount of advertising expenditures. The sales manager thinks that sales volume and advertising expenditures are modeled according to the following linear equation. Both sales volume and advertising expenditures are in thousands of dollars. Estimated Sales Volume=46.41+0.45(Advertising Expenditures) If the company has a target sales volume of $200,000, how much should the sales manager allocate for advertising in the budget? Round your answer to the nearest dollar.
Final answer:
The sales manager should allocate approximately $341,310 for advertising to achieve the target sales volume of $200,000. This amount is determined by using the linear equation provided and solving for the advertising expenditures.
Explanation:
To find out how much the sales manager should allocate for advertising expenditures to achieve a target sales volume of $200,000, we use the given linear equation:
Estimated Sales Volume = 46.41 + 0.45(Advertising Expenditures)
First, we convert the target sales volume to thousands of dollars - which would be $200 (since $200,000 is in thousands), and then plug it into the equation:
200 = 46.41 + 0.45(Advertising Expenditures)
Next, we solve for Advertising Expenditures:
200 - 46.41 = 0.45(Advertising Expenditures)
153.59 = 0.45(Advertising Expenditures)
Advertising Expenditures = 153.59 / 0.45
Advertising Expenditures = 341.31
Therefore, the sales manager should allocate approximately $341,310 for advertising in the budget to achieve the target sales volume of $200,000. This value is rounded to the nearest dollar as requested.
To achieve a target sales volume of $200,000, the company should allocate approximately $341,310 for advertising.
To determine the amount to allocate for advertising to reach a target sales volume of $200,000, we use the provided linear equation:
⇒ Estimated Sales Volume = 46.41 + 0.45(Advertising Expenditures)
First, set the estimated sales volume to 200 (since the sales volume is in thousands of dollars):⇒ 200 = 46.41 + 0.45(Advertising Expenditures)
Next, solve for Advertising Expenditures:Subtract 46.41 from both sides:⇒ 200 - 46.41 = 0.45(Advertising Expenditures)
⇒ 153.59 = 0.45(Advertising Expenditures)
Divide both sides by 0.45:⇒ Advertising Expenditures = 153.59 ÷ 0.45
⇒ Advertising Expenditures ≈ 341.31
Therefore, the company should allocate approximately $341,310 (rounded to the nearest dollar) for advertising expenditures to achieve the target sales volume of $200,000.
Complete question:
Suppose that a company wishes to predict sales volume based on the amount of advertising expenditures. The sales manager thinks that sales volume and advertising expenditures are modeled according to the following linear equation. Both sales volume and advertising expenditures are in thousands of dollars.
Estimated Sales Volume = 46.41 + 0.45(Advertising Expenditures)
If the company has a target sales volume of $200,000, how much should the sales manager allocate for advertising in the budget? Round your answer to the nearest dollar.
simplify -3(x+3)+5(4x+6)
Answer:
17x +21
Step-by-step explanation:
-3(x+3)+5(4x+6)
Distribute
-3x-9+20x+30
Combine like terms
17x +21
A chef planning for a large banquet thinks that 2 out of every 5 dinner guests will order his soup appetizer. He expects 800 guests at the banquet. Use equivalent ratios to estimate how many cups of soup he should prepare. A chef planning for a large banquet thinks that 2 out of every 5 dinner guests will order his soup appetizer. He expects 800 guests at the banquet. Use equivalent ratios to estimate how many cups of soup he should prepare.
Answer:
320
Step-by-step explanation:
2/5 = .4
800 * .4 =320
X and y are supplementary angles. Y measures 88 what is the measure of X
Answer:
x = 92
Step-by-step explanation:
Supplementary angles add to 180 degrees,
x+y = 180
We know y =88
x+88 = 180
Subtract 88 from each side
x+88-88=180-88
x =92
Assume the random variable X is normally distributed with mean mu equals 50 and standard deviation sigma equals 7. Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded. Upper P (Upper X greater than 34 )
Answer:
[tex]P(X>34) = 0.9889[/tex]
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 50
Standard Deviation, σ = 7
We are given that the distribution of random variable X is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
P(X greater than 34)
[tex]P( X > 34) = P( z > \displaystyle\frac{34 - 50}{7}) = P(z > -2.2857)[/tex]
[tex]= 1 - P(z \leq -2.2857)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(X>34) = 1 - 0.0111= 0.9889= 98.89\%[/tex]
The attached image shows the normal curve.
25 points) A credit card company has a Refer-a-Friend program in which each member is assumed to successfully refer a friend at an exponential rate of λ per member. Each member cancels membership at an exponential rate of μ. If the total number of members is less than N, the credit card company will advertise online, and additional customers will join at an exponential rate of θ due to the advertising. If the total number of members is greater or equal to N, the credit card company will stop advertising, and customers will only join through the referral program.
(a) Set this up as a birth and death model. That is clearly define the states and transition rates. Draw rate diagram.
(b) Set up balance equations to be solved to find P's for 1 2 0. Do not solve them.
(C) Let N = 30, express the proportion of time that customers will get the credit card of the company through referral program in terms of P's.
Answer:
Step-by-step explanation:
See attached file for answer pls
What is the simplified form of this expression?
(-3x2 + 4x) + (2x2 − x − 11)
A.
-x2 + 5x − 11
B.
-x2 + 3x – 11
C.
-x2 + 3x + 11
D.
-x2 + 5x + 11
Answer:
−x2+3x−11
Step-by-step explanation:
−3x2+4x+2x2−x−11
(−3x2+2x2)+(4x−x)−11
−x2+3x−11
Answer:
Step-by-step explanation:
Hope this Helps ;)
A hand consists of 1 card drawn from a standard 52-card deck with flowers on the back and 1 card drawn from a standard 52-card deck with birds on the back. A standard deck has 13 cards from each of 4 suits (clubs, diamonds, hearts, spades). The 13 cards have face value 2 through 10, jack, queen, king, or ace. Each face value is a "kind" of card. The jack, queen, and king are "face cards."
A.How many different hands are possible? (Note that a flower-ace-of-spades, bird-queen-of-hearts and a flower-queen-of-hearts, bird-ace-of-spades are two different outcomes.)
B.How many hands consist of a pair of aces?
C.How many hands contain all face cards?
D.How many hands contain exactly 1 king?
E.How many hands consist of two of a kind (2 aces, 2 jacks, and so on)?
F.. How many hands contain at least 1 king?
Answer:
A) 2704 hands
B) 16 hands
C) 144 hands
D) 384 hands
E) 208 hands
F) 400 hands
Step-by-step explanation:
See the attached file for explanation
There are 2704 possible hands, 16 hands consist of a pair of aces, 144 hands have all face cards, 384 hands have 1 king, 208 hands consist of two of a kind, and 384 hands contain at least 1 king.
Explanation:To answer these probability related questions, we must look at the combinations which we can draw. A standard deck contains 52 cards and the hand in question consists of 1 card from 2 different decks, so:
A. The total number of different hands possible is 52 * 52 = 2704.
B. There are 4 aces in each deck so there are 4 * 4 = 16 hands that consist of a pair of aces.
C. A deck has 12 face cards and since 2 cards are being drawn, the number of hands with all face cards is 12 * 12 = 144.
D. The number of hands with exactly 1 king is found by multiplying the number of kings in a deck (4) by the number of non-kings in a deck (52-4). So, 4 * 48 = 192, but we must consider this happening in both decks: so 2 * 192 = 384.
E. For two of a kind hands (2 aces, 2 kings etc.), there are 13 kinds, thus 13 * 4 * 4 = 208.
F. For at least 1 king, either the first card or second card can be a king, so we use similar mathematics as used in D, which is 2 * 192 = 384.
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Mr. Diaz wants to cut a sandwich into fourths to share with his family Drawn Lines in the Square to show One Way Mr Gs can cut the sandwich into forts
How to solve -222=5x-3(-7y-4)
Answer:
x=46 4/5, x=46.8
Step-by-step explanation:
To find x-intercept/zero, substitute y=0
-222=5x-3(-7*0-4)
-222=5x-3(-7*-4) Solve
x= -234/5
x=46 4/5, x=46.8
What is the volume of this rectangular prism
Answer:
2
Step-by-step explanation:
Multiply all of the fractions together.
A package is in the shape of a triangular prism. The bases are right triangles with perpendicular legs measuring 9 cm and 12 cm.The distance between the bases in 10 cm
Answer:
I think that the answer is either A or C. I'm not too sure on which one.
Step-by-step explanation
How many 5-digit numbers are there that are divisible by either 45 or 60 but are not divisible by 90?
There are 7,991 5-digit numbers that are divisible by either 45 or 60 but not divisible by 90.
Explanation:To find the number of 5-digit numbers that are divisible by either 45 or 60 but not by 90, we can use the principle of inclusion-exclusion. First, let's find the number of 5-digit numbers divisible by 45 and the number divisible by 60, then subtract the number divisible by 90 to avoid overcounting.
A 5-digit number divisible by 45 must also be divisible by 9 and 5. The smallest 5-digit number divisible by 45 is 10005 (9 * 5 * 445), and the largest is 99990 (9 * 5 * 2222). We can find the number of 5-digit numbers divisible by 45 by subtracting the two numbers and adding 1 (99990 - 10005 + 1).
A 5-digit number divisible by 60 must also be divisible by 12 and 5. The smallest 5-digit number divisible by 60 is 10020 (12 * 5 * 167), and the largest is 99960 (12 * 5 * 833). We can find the number of 5-digit numbers divisible by 60 using the same method as before (99960 - 10020 + 1).
Finally, we subtract the number of 5-digit numbers divisible by 90. A 5-digit number divisible by 90 must be divisible by 45 and 2. The smallest 5-digit number divisible by 90 is 10035 (9 * 5 * 445 and 2 * 5017), and the largest is 99945 (9 * 5 * 2221 and 2 * 49973). Again, we use the same method as before to find the number of 5-digit numbers divisible by 90 (99945 - 10035 + 1).
To find the final answer, we subtract the number of 5-digit numbers divisible by 90 from the sum of the numbers divisible by 45 and 60.
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An online retailer wants to estimate the number of visitors that click on their advertisement from a particular website. Of 978 page views in a day, 8% of the users clicked on the advertisement. Create a 90% confidence interval for the population proportion of visitors that click on the advertisement.
Answer:
(0.0657,0.0943) is the 90% confidence interval for the population proportion of visitors that click on the advertisement.
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 978
Percentage of users that clicked on advertisement = 8%
Sample proportion:
[tex]\hat{p} = 0.08[/tex]
90% Confidence interval:
[tex]\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
[tex]z_{critical}\text{ at}~\alpha_{0.10} = 1.645[/tex]
Putting the values, we get:
[tex]0.08\pm 1.645(\sqrt{\dfrac{0.08(1-0.08)}{978}})\\\\= 0.08\pm 0.0142\\\\=(0.0658,0.0942) = (6.57\%,9.43\%)[/tex]
(0.0657,0.0943) is the 90% confidence interval for the population proportion of visitors that click on the advertisement.
What is the measure of each angle in the Summer Triangle
The measure of each angle in the Summer Triangle depends on the position and alignment of the stars and cannot be determined without specific coordinates and time of observation.
Explanation:The Summer Triangle is a prominent summer asterism formed by three bright stars: Vega, Deneb, and Altair. The measure of each angle in the Summer Triangle depends on the position and alignment of these stars in the sky. The angles cannot be determined without the specific coordinates and time of observation.
Astronomers use angles to measure the separation between celestial objects in the sky. A full circle has 360°, and the half-sphere of the sky from horizon to opposite horizon contains 180°. By measuring the angular separation between two stars or objects, astronomers can determine how far apart they appear in the sky. The angle is typically measured in degrees (°).
For example, if two stars are 18° apart, their separation spans about 1/10 of the dome of the sky. To give you a sense of how big a degree is, the full Moon is about half a degree across, which is similar to the width of your smallest finger (pinkie) seen at arm's length.
What are numbers that are positive negative and 0 that are not irrational
Answer:
Any number that is not a fractional value positive and negative but technically all numbers are irrational
Step-by-step explanation:
Any number that is not a fractional value positive and negative but technically all numbers are irrational.
We have to find the numbers that are positive negative and 0 that are not irrational
What is the fractional value positive?
Fractional values are represented using fixed-point arithmetic and are useful for DSP applications.
For a fractional division, we first scale the denominator to the range 0.5 ≤ d < 1.0.
Then we use a table lookup to provide an estimate of x0 to d−1.
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A fence is to be built to enclose a rectangular area of 450450 square feet. The fence along three sides is to be made of material that costs $33 per foot. The material for the fourth side costs $99 per foot. Find the dimensions of the rectangle that will allow for the most economical fence to be built.
Answer:
The dimensions of the rectangle that will allow for the most economical fence to be built are 30x15 feets, where two sides of 30 feets long cost $33 each one per foot, one side of 15 feets costs also $33 and the remaining side costs $99
Step-by-step explanation:
If x and y were the dimensions of the rectangle (in feets), then we have that x*y = 450. Therefore, y = 450/x.
Note that the rectangle as a result is formed by 2 sides with length x and 2 other sides with length 450/x. Lets suppose that x is the length of the 2 sides that costs both $33 and the other two sides, which have length 450/x, one costs also $33 and the other costs $99.
The cost, in $, function f,in terms of x, is given as follows
[tex] f(x) = 2 * 33 * x + 33*\frac{450}{x} + 99*\frac{450}{x} = 66x + \frac{59400}{x} [/tex]
We want to minimize f, so we will derivate it and equalize the derivate to 0:
[tex] f'(x) = 66 - \frac{59400}{x^2} [/tex]
[tex] f'(x) = 0 \leftrightarrow 66 = \frac{59400}{x^2} \leftrightarrow x^2 = \frac{59400}{66} = 900 \leftrightarrow x = \sqrt{900} = 30 [/tex]
(Note that x cant be negative, so in the equation we didnt count the opposite of the square root of 900)
We concluded that one dimension is 30 feets, and the other should be 450/30 = 15.
Graph the line that passes through the points (3, -2)(3,−2) and (9, 2)(9,2) and determine the equation of the line.
Answer:
2x -3y = 12
Step-by-step explanation:
For some horizontal change Δx and some vertical change Δy between the two points, an equation of the line through points (x1, y1) and (x2, y2) can be written as ...
Δy·x -Δx·y = Δy·(x1) -Δx·(y1)
Here, we have ...
Δy = y2 -y1 = 2 -(-2) = 4
Δx = x2 -x1 = 9 -3 = 6
So, our equation can be ...
4x -6y = 4·3 -6·(-2) = 24
Factoring out a common factor of 2 makes the equation be ...
2x -3y = 12 . . . . . . equation of the line in standard form
Solving for y gives the equation in slope-intercept form:
y = 2/3x -4
_____
More conventional solution
Plotting the points and drawing the line, you see that the y-intercept is -4. You also see that there is a "rise" of 2 grid squares for each "run" of 3 grid squares. Thus the slope of the line is 2/3. With this information, you can write the equation directly in slope-intercept form:
y = mx + b . . . . . . line with slope m and y-intercept b
y = 2/3x -4 . . . . . . the line through the given points
Final answer:
The line passing through the points (3, -2) and (9, 2) has a slope of 2/3, and its equation is y = (2/3)x - 4, which can be graphed by plotting the given points and ensuring the slope is represented correctly.
Explanation:
To graph the line that passes through the points (3, -2) and (9, 2), we first find the slope of the line. The slope formula is (y2 - y1) / (x2 - x1). Plugging in our points, we get (2 - (-2)) / (9 - 3) which simplifies to 4 / 6, further reduced to 2 / 3. Therefore, the slope of the line is 2 / 3.
Next, we use one of the points and the slope to write the equation in point-slope form, y - y1 = m(x - x1). Using the point (3, -2), the equation becomes y + 2 = (2/3)(x - 3). After distributing the slope and moving -2 to the other side, we get the equation y = (2/3)x - 4.
Finally, we can graph the line by plotting the two given points and drawing a straight line through them, ensuring that the rise over the run matches the slope of 2 / 3. The equation of the line y = (2/3)x - 4 can be verified using various x-values to see if the resulting y-values fall on the line plotted.
Simplify. 2√27 − √48 +4√12
Answer:
= 10√3
Step-by-step explanation:
[tex]2 \sqrt{27} - \sqrt{48} + 4 \sqrt{12} \\ = (2 \times \sqrt{9 \times 3}) - (\sqrt{16 \times 3}) + (4 \times \sqrt{4 \times 3} )\\ = (2 \times 3 \sqrt{3}) - 4 \sqrt{3} + (4 \times 2 \sqrt{3} ) \\ = 6 \sqrt{3} - 4 \sqrt{3} + 8 \sqrt{3} \\ = 10 \sqrt{3} [/tex]
Answer:
10√3
Step-by-step explanation:
2√27 − √48 + 4√12
2√(3²×3) − √(4²×3) + 4√(2²×3)
6√3 − 4√3 + 8√3
√3(6 - 4 + 8)
10√3
Banks can create money by making use of:
Answer:
Loans
Step-by-step explanation:
I don´t know how to explain it,and I hope my answer is correct though.
Answer:
banks create money by issuing loans and opening checking accounts
Step-by-step explanation:
A slice of pizza costs $3.50. You have $25.00 in your wallet to spend on pizza. Write an inequality to represent the number, p, of slices of pizza you can buy.
Answer:
[tex]25.00\geq 3.50p[/tex]
Step-by-step explanation:
since you have $25.00, you can only spend up to that much money, so it will have to be less than or equal to , and since p = slices of pizza, you multiply that by 3.50 to know how much you can buy.
hope this helps :)
Answer:
$3.5p<=$25.00
Step-by-step explanation:
If you only have $25.00 to spend on pizza it can not exceed that limit, so your total amount needs to be more than or equal to money the pizza slices cost
Write the values of each of the digits in 6,582,390,417 in word form
The solution is: 6,582,390,417 in word form is, six billon five hundred eighty two million three hundred thousand and ninety four hundred seventeen.
What is place value?Place value is the basis of our entire number system. This is the system in which the position of a digit in a number determines its value.
The number 42,316 is different from 61,432 because the digits are in different positions.
here, we have,
given that,
6,582,390,417
so, the values of each of the digits in 6,582,390,417 in word form is:
6: six billon
5: five hundred
8: eighty two million
3: three hundred thousand
and ninety four hundred
seventeen.
Hence, The solution is: 6,582,390,417 in word form is, six billon five hundred eighty two million three hundred thousand and ninety four hundred seventeen.
To learn more on place value click:
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8 subtracted from x is less then or equal to 17
Answer:
it can be written in eqn form as
x-8=>17
or,x=>25
Answer:
x-8 ≥17
If you need to find x, Add 8 on both sides
x ≥25
Hope this helped
What does the 99% confidence level in the previous problem tell us? Group of answer choices There is a 99% chance that this particular interval contains the population proportion. The interval will contain 99% of all sample proportions. Of confidence intervals with this margin of error, 99% will contain the population proportion. Of confidence intervals with this margin of error, 99% will contain the sample proportion.
Answer:
The confidence interval for the mean is given by the following formula:
[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]
The margin of error is given by:
[tex] ME= z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]
For this case since the confidence is 99% we are confident that the true proportion of interest would be on the interval calculated and the best option for this case is:
Of confidence intervals with this margin of error, 99% will contain the population proportion
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
Solution to the problem
The confidence interval for the mean is given by the following formula:
[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]
The margin of error is given by:
[tex] ME= z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]
For this case since the confidence is 99% we are confident that the true proportion of interest would be on the interval calculated and the best option for this case is:
Of confidence intervals with this margin of error, 99% will contain the population proportion