"We are 95% confident that the mean sodium content for all beef hot dogs is between 353.2 and 449.1 mg." is the correct statement.
The true parameter must be properly and contextually stated.
We are researching confidence intervals for population means rather than for particular observations. The parameter is, to put it in plain English, the average sodium content of all beef hot dogs. The phrase "We are 95% confident" would be a better translation.
Thus the correct statement is as mentioned above.
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A plane is on its approach to land on the runway. The jet's height above the ground is given in feet as a function of
the time in seconds. The following table tracks the plane as it lands:
t (in seconds) h (in feet)
0
4000
5
3500
10
3000
15
20
25
2500
2000
1500
Mark this and return
=
Ah
4
Calculate the slope. Use the formula
a. The plane is losing altitude.
b. The plane is gaining altitude.
c. The plane is remaining at a constant height.
d. The plane is losing altitude at a rate of 500 feet/second.
At
What is the significance of the sign of the slope?
Save and Exit
Next
Submit
The slope Using the formula will be h = -100t + 4000
This is a linear function because for every 5 seconds that pass, the height of the plane drops 500 feet, or -500 to be exact. So that's the slope of the line.
If we look at the table we can determine where the graph goes through the h axis. The h axis is the y axis, and the t axis is the x axis. So where the graph goes through the h axis is also the y-intercept.
If your teacher is any good at all, he/she would make sure that you understand beyond a shadow of a doubt that the y-intercept exists where x = 0. Looking at the table, where x (t) is 0, y (h) is 4000 feet.
Writing the linear equation then is super easy. In the form y = mx + b, we already know both the slope (-100) and the y-intercept (4000), so we fill in accordingly:
h = -100t + 4000 which appears to be choice a.
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1. Why is identifying
the domain and range important when
defining a function?
Identifying the domain and range is important when defining a function because domain gives all the input values and range gives all the output values a function can take. It is very essential to know domain and range of a function.
Domain are represented by independent variable and are graphed on x coordinate of the axis.
Range are dependent values and are graphed on y axis of the graph.
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a data analyst is using statistical measures to get a better understanding of their data. what function can they use to determine how strongly related are two of the variables?
The correlation coefficient can be used to get a better understanding and to determine the extent of a strong relation between two variables.
In a statistical setting, two or more variables are said to be connected if their values fluctuate in such a way that as the value of one variable rise or falls, the value of the other variable does the same (although it may be in the opposite direction).
For instance, there is a relationship between the two variables "hours worked" and "revenue earned" if a rise in hours worked is correlated with an increase in income earned. When considering the two factors "price" and "purchasing power," the ability of a person to purchase items reduces as the price of those goods rises (assuming a constant income).
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a student in public administration wants to estimate the mean monthly earnings of city council members in large cities. she can tolerate a margin of error of $100 in estimating the mean. she would also prefer to report the interval estimate with a 95% level of confidence. the student found a report by the department of labor that reported a standard deviation of $1,000. what is the required sample size? (hint: round your answer up to the nearest whole number)
the required sample size for the interval estimate with a 95% level of confidence is 385
since we are given the margin of error which is f $10 and a standard deviation which is $1,000, and we are also given the level of confidence which is 95%
so the formula we are referring to calculate the sample size is :
n=z(0..95)*s²/ E
here, E is the margin of error, S is the standard deviation
so z score of 0.95 is 1.96
so n = 1.96*1000^2/100
= 384.16 ,which is almost 385
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A thermostat in a house regulates when the heater turns on and off. The heater turns on then
the house is 4° below the set temperature and turns off when the house is 4° above the set
temperature. The temperature is set at 68°. At 10:15am the heater turns on, and at 10:30am the
heater turns off. Write a sinusoid that models the change in temperature in the house.
The sinusoid that models 4° = A cos B(x - C) and 68° = A cos B(x - C) the change in temperature in the house.
The heater turns on when the house is 4° below the set temperature and turns off when the house is 4° above the set temperature. The temperature is set at 68°. At 10:15 am the heater turns on, and at 10:30 am the heater turns off.
Temperature fluctuations can be modeled using the sine and cosine functions throughout the day.
The equations that can be used to model these data is of the form:
At 10:30 am the heater turned off,
⇒ 4° = A cos B(x - C)
At 10:15 am the heater turned on,
⇒68° = A cos B(x - C)
where A, B, and C are constants, y is the temperature in °C and x is the time
Thus, The sinusoid that models 4° = A cos B(x - C) and 68° = A cos B(x - C) is the change in temperature in the house.
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17. If a = 3b^2 and a = 27, what is one value of b?
4.5
9
1.73
3
Answer:
b = 3
Step-by-step explanation:
Given that,
→ a = 27
Forming the equation,
→ 27 = 3b²
Now the value of b will be,
→ 27 = 3b²
→ b² = 27/3
→ b = √9
→ [ b = 3 ]
Hence, the value of b is 3.
⇒Given that a=27 in the equation [tex]a=3b^{2} \\[/tex] in the place of a plug in 27 and solve for b
[tex]27=3b^{2} \\\frac{27}{3} =\frac{3b^{2}}{3} \\b^{2} =9\\b^{2}-9=0\\(b+3)(b-3)=0\\b+3=0\\or\\b-3=0\\b=-3\\or\\b=3[/tex]
⇒Note b can also be -3 but the only option available as the answer is 3
∴ b=3 in this case.
Graph the equation by using the slope intercept method
For the given equation 4x + 3y =21 the slope intercept form is given by y = (-4/3)x + 7.
Graph is attached.
As given in the question,
Given equation is equal to :
4x + 3y = 21
To get the slope intercept form of the given equation we have,
Subtract 4x from both the sides of the given equation we have,
4x + 3y - 4x = 21 - 4x
⇒ 3y = 21 - 4x
Now divide by 3 on both the sides of the equation we get,
3y / 3 = (-4/3)x + (21/3)
⇒ y = (-4/3) x + 7
Graph of the given equation in slope intercept form y = (-4/3) x + 7 is attached.
When x = 0 ⇒ y = 7
y= 0 ⇒ x = 21 /4
Therefore, for the given equation 4x + 3y =21 the slope intercept form is given by y = (-4/3)x + 7.
Graph is attached.
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3b(2x-z^3)=2h-7gx change the subject to x
Answer:
Step-by-step explanation:
3b(2x - z^3) = 2h - 7gx Distribute 3b
6bx - 3bz^3 = 2h - 7gx Add 3bz^3 to both sides
6bx = 3bz^3 + 2h - 7gx Add 7gx to both sides
6bx + 7gx = 3bz^3 + 2h Factor left side, factor out a gcf of x
x(6b + 7g) = 3bz^3 + 2h Divide both sides by (6b + 7g) to isolate x
x = (3bz^3 + 2h)/ (6b + 7g)
Decrease 330 km by 54%.
Answer: 151.8
Step-by-step explanation:
330/100 x 54 = 178.2
330- 178.2 = 151.8
a popular resort hotel has 300 rooms and is usually fully booked. about 6% of the time a reservation is cancelled before the 6:00 p.m. deadline with no penalty. what is the probability that at least 275 rooms will be occupied? use the binomial distribution to find the exact value. a. 0.01 b. 0.96 c. 0.93 d. 0.85
When binomial distribution is used, the probability that at least 275 rooms are occupied is 0.96
Option b. is correct
We have the following parameters:
sample, n=300
proportions of rooms reserved, p=6%
We first get the sample mean,
Sample mean=n*p
=300*6%
=18
Now, we get population mean according to binomial distribution, μ'
μ=n-sample mean
=300-18
=282
We get the standard deviation, σ
σ=(sample mean*(1-p))^1/2
=(18*(1-6%))^1/2
=4.11
We now, calculate z-score:
z=(x-μ)/σ, given x should be at least 275
z=(275-282)/4.11
=-1.703
Now, we have p(x>275)=p(z>-1.703)
From z-score of probabilities, we have p(z>-1.703) as 0.95572
So, p(x>275)=0.95572
=0.96
Hence, the probability that at least 275 rooms are occupied is 0.96
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An angle is bisected. Each resulting angle is 78 degree. how is the original angle
List all factors of the numerator and denominator. Use gcf method to simplify Creduce) each fraction. You must show work
The reduced fraction is 6/7 using GCF method.
What is GCF method?
The largest number, which is the factor of two or more number is called the Greatest Common Factor (GCF). It is the largest number (factor) that divide them resulting in a Natural number. Once all the factors of the number are found, there are few factors which are common in both. The largest number that is found in the common factors is called the greatest common factor. The GCF is also known as the Highest Common Factor (HCF)
Given,
the fraction = 24/28.
the factors of 24 = 2×2×2×3
The factors of 28 = 2×2×7
The gcf is 2 × 2 = 4
divide the denominator and numerator by 4
24 ÷ 4 = 6
28÷ 4 = 7
We get,
the fraction = 6/7.
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how does the symmetry of a parabolas hep you graph a quadratic function?
The axis of symmetry is the line that is relative is vertical goes through the vertex of a parabola so the left and right sides of the parabola are symmetric. To simplify, this line that is relative the graph of a equation that is quadratic two mirror images.
Equation of the Axis of Symmetry of a Parabola:
The equation for the axis of symmetry of a parabola can be expressed as:
[tex]x=\frac{-b}{2a}[/tex]
Remember that every quadratic function can be written in the standard form [tex]y = ax^{2}+bx+c[/tex] . The graph of a quadratic function is called a parabola, where every point on that parabola represents an x and a y that solves the quadratic function.
The vertex of a quadratic function is the highest or lowest point on the graph. The coordinate of the vertex of the parabola, then, is the x and y solution for the lowest or highest point of the parabola.
Calculating the Axis of Symmetry of a Parabola:
Again, the axis of symmetry of the parabola is the line on the graph that passes through the vertex of the parabola and splits the graph into two symmetrical sides.
It is expressed as:
[tex]x=\frac{-b}{2a}[/tex]
Or x = -2 after you substitute in the values for a and b.
Finding the Vertex of a Parabola:
To find the actual coordinates for the vertex of the parabola, simply substitute the x value into the polynomial expression to find the corresponding y value. Remember, each point on the quadratic graph is a solution to the equation.
When we continue with the previous example, we know that x = -2.
We substitute that value for x in the original quadratic function.
[tex]y=x^{2} +4x+3\\y=(-2)^{2}+4(-2)+3\\ y=4+(-8)+3[/tex]
Solving it gives us y = -1. We now know that the vertex of the parabola is the coordinate (-2, -1). Finding the vertex of a parabola couldn’t be easier.
How To Find Axis of Symmetry?
Here's what you need to remember: Whether you’re after the axis of symmetry or the full coordinates of the vertex of the parabola, use this formula to start graphing a quadratic equation.
[tex]x=\frac{-b}{2a}[/tex]
Solving for x gives you the axis of symmetry. This line of symmetry will intersect with the parabola at its vertex, where x is the coordinate you just calculated and y is the coordinate when you substitute x back into the quadratic equation,
[tex]y = ax^{2}+bx+c[/tex].
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8+ (-3) + (-8)
NEED HELP
Answer:
[tex]-3[/tex]
Step-by-step:
[tex]8+ (-3) + (-8)[/tex]
1 ) Combine like terms...
[tex]=5 - 8[/tex]
2 ) Solve...
[tex]= - 3[/tex]
Hope this helps! :)
The number of computer security breaches is expected to increase at a yearly rate of
86%.
Use the exponential growth model to determine the equivalent monthly rate.
Enter the rate, to the nearest tenth of a percent, in the box.
Write an expression for the following situation: 4 less than 20 times some number.
A. 20-x-4
B. 20 + x - 4
C. 20x - 4
D. 20 - x + 4
Answer: D
Step-by-step explanation: Took the test
Explain how the equations 2/3m=-4 and -4m=24 are equivalent?
Both 2/3m=-4 and -4m=24 have a solution of 1/6 and are equivalent
What are algebraic expressions?Algebraic expressions are described as expressions that contains terms, variables, coefficients, constants and factors.
They are also known to be made up of some arithmetic operations, such as;
AdditionSubtractionMultiplicationDivisionBracket ParenthesesWe have the equations;
2/3m=4 and -4m=24
Let's solve for m in the first equation
12m = 2
Divide both side by coefficient of m
m = 2/ 12 = 1/ 6
For the second equation
-4m = 24
Divide both sides by - 4
m = 24/-4
m = 6/ -1
Take inverse
m = 1/6
Hence, the equations are equivalent
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Select the two values of x that are roots of this equation. x2 + 3x – 5 = 0
The two values of x which are root of the given equation are; x = (-3 + √29)/2 and x = (-3 - √29)/2.
What are the two values of x which are root of the given quadratic equation?It follows from the task content that the two values of x which are roots of the given quadratic equation be determined.
Recall that the roots of quadratic equations are given by the formula;
x = {-b ± √(b² - 4ac)} / 2a
Since the given equation is; x² + 3x - 5; it follows that; a = 1, b = 3 and c = -5.
Therefore, the roots are as follows;
x = {-3 ± √(3² - 4•1•-5)} / 2(1)
x = (-3 ± √29)/2
Therefore, the required roots are;
x = (-3 + √29)/2 and x = (-3 - √29)/2
Ultimately, the roots of the given quadratic equation x² + 3x - 5 are; x = (-3 + √29)/2 and x = (-3 - √29)/2.
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Find x if AC= 17, BD = 2x - 6, AD= x + 16, and BC = 6
Answer:
Hey, hope it helps my friend
Step-by-step explanation:
In the image
Hey, I haven't been able to get any of these right, I wasn't a there the day we learned this and i'm needing help getting the rest of it done before 3:00. Could any of you please help me out on this, it'd mean a lot!
The correct graph for each of the equations are respectively;
5) Graph C
6) Graph A
7) Graph B
How to Interpret Linear Equation Graphs?The general form of equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
5) We are given the linear equation as;
-9x + 3y = 0
3y = 9x + 0
y = 3x + 0
The slope is 3 and y-intercept is zero. Thus, the correct graph for this function is; Graph C
6) We are given the linear equation as;
4x - 6y = 12
Rearranging we have;
6y = 4x - 12
y = ⁴/₆x - 2
y = ²/₃x - 2
Thus, slope is 2/3 and y-intercept is -2. The correct graph is graph A
7) The correct graph of the function 25x - 10y = -50 is the graph B.
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the p-value is a. a sample statistic. b. the same as the z statistic. c. a distance. d. a probability.
The p - value is d ) a probability .
Defining P - Value
P - Value : It is the probability of obtaining results at least as extreme as the observed results of a statistical hypothesis test , assuming that the null hypothesis is correct . The p - value does not , in itself , establish probabilities of hypotheses . Rather , it is a tool for deciding , whether to reject null hypothesis or not .
A smaller p - value means that there is stronger evidence in favor of alternative hypothesis .
Hence , the p - value is d ) a probability .
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Marsha deposited $5500 into a savings account 4 years ago. The simple interest rate is 5% How much money did Marsha earn earn in interest?
Marsha deposited $5500 into savings with 5% interest rate
1st year, Marsha will earn : [tex]0.05 \times 5500 = 275[/tex]
2nd year, Marsha will earn: [tex]0.05 \times 5775 = 288.75[/tex]
3rd year, Marsha will earn: [tex]0.05 \times 6063.75 = 303.19[/tex]
4th year, Marsha will earn: [tex]0.05 \times 6366.94 = 318.35[/tex]
What causes an echo?
rarefaction
reflection
refraction
Answer:
Reflection
Step-by-step explanation:
Reflection is like looking at yourself through a mirror, so it would be the same for sound.
Tell me if this is correct.!
Answer:
Reflection
Step-by-step explanation:
i took this quiz
What is the equation of the line that passes through the point (6,-5) and has a slope of -{1}{3}?
Answer:
y = - [tex]\frac{1}{3}[/tex] x - 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - [tex]\frac{1}{3}[/tex] , then
y = - [tex]\frac{1}{3}[/tex] x + c ← is the partial equation
to find c substitute (6, - 5 ) into the partial equation
- 5 = - 2 + c ⇒ c = - 5 + 2 = - 3
y = - [tex]\frac{1}{3}[/tex] x - 3 ← equation of line
For her final project, stacy plans on surveying a random sample of students on whether they plan to go to florida for spring break. From past years, she guesses that about % of the class goes. Is it reasonable for her to use a normal model for the sampling distribution of the sample proportion? why or why not?.
Yes, it is reasonable for her to use a normal model for the sampling distribution of the sample proportion. In this case, less than ten efforts have been successful. Since 5 is a lot less than 10, this is the case.
Because the data don't fit the success and failure criteria, it is not appropriate to adopt a normal model for a sampling of the sample distribution.
50 students make up the sample. The probability that she assumes 10% of the group will attend is 10%.
It will be demonstrated by:
1 - p = 1 - 10% = 1 - 0.10 = 0.90
np = 50 × 0.1 = 5. This suggests the number of victories.
Less than 10 attempts have succeeded in this instance. 5 is much less than 10, hence this case. As a result, the data does not satisfy the requirement.
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The question is -
For her final project, Stacy plans on surveying a random sample of 50 students on whether they plan to go to Florida for spring break. from past years, she guesses that about 10% of the class goes. is it reasonable for her to use a normal model for the sampling distribution of the sample proportion? why or why not?
answer please will give 20 points
Answer:plot the point (2,5)
Step-by-step explanation:
write the quotient as a power. a^21/a
the quotient as a power. a^21/a is a^20.
What is Power?
In mathematics, power defines a base number raised to the exponent, where base number is the factor which is multiplied by itself and exponent denotes the number of times the same base number is multiplied.
What is quotient?
The number we obtain when we divide one number by another is the quotient.
What is exponential function?
An exponential function is a mathematical function of the following form: f ( x ) = a x. where x is a variable, and a is a constant called the base of the function. The most commonly encountered exponential-function base is the transcendental number e , which is equal to approximately 2.71828.
Given that,
a^21/a
quotient as power = a^21/a
= a^(21-1)
= a^20
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What is the diameter of a circle with a circumference of 47.1 in.?
A. 7.5 in.
B. 15 in.
C. 0.75 in.
D. 1.5 in.
The required diameter of the circle is given as 15 in. Option B is correct.
Given that,
The circumference of a circle is given 47.1 in, we have to determine the diameter of the circle.
Perimeter is the measure of the figure on its circumference.
Here,
As per the given condition,
First, write the formula for the circumference of the circle,
Circumference of the circle = πD
now substitute the value in the above equation,
47.1 = 3.14 D
D = 47.1/3.14
D = 15 in
Thus, the required diameter of the circle is given as 15 in. Option B is correct.
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PLEASE HELP ME THIS IS DUE TOMORROW!!!!!!!!
(a) The scatter plot and the line of fit are shown in the graph.
(b) The equation of the line of fit is y = -2.5x+18.3.
(c) The slope is -2.5 which indicates that the gamer losses 2.5 every week after getting a new game.
What is a scatter plot?A scatter plot is a graph of the given points or given data.
(a)
To make a scatter plot of the data, plot the points (x,y) on a graph.
To draw the line of fit, draw a line such that the distance between the line and the plotted points is minimum.
(b) The line passes through points (7.3,0)and (0,18).
The equation of the line is given by:
[tex]y-y_1=\frac{(y_2-y_1)}{(x_2-x_1)}(x-x_1)[/tex]
Substitutes the points (x₁,y₁) = (7.3,0) and (x₂,y₂)=(0,18) into the above equation:
[tex]y-0=\frac{18-0}{0-7.3}(x-7.3)\\y=-2.5(x-7.3)\\y=-2.5x+18.3[/tex]
(c) The slope of a line of the form y=mx+c is m.
Therefore, the slope of the line y=-2.5x+18.3 is m = -2.5.
The slope indicates the change in y with respect to the change in x.
Therefore, the slope -2.5 indicates that the gamer losses 2.5 every week after getting a new game.
Hence,
(a) The scatter plot and the line of fit are shown in the graph.
(b) The equation of the line of fit is y = -2.5x+18.3.
(c) The slope is -2.5 which indicates that the gamer losses 2.5 every week after getting a new game.
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10p^2 - 20p - 34 = -4
Answer:
p = -1 ; p= 3
Step-by-step explanation:
10p^2 - 20p - 34 +4 = 0
10p^2 -20p - 30 = 0
10/10 p^2 - 20/10 p - 30/10 = 0
p^2 - 2p - 3 = 0
(p-3)(p+1) = 0
p = 3
p = -1
