Answer:
GH = 6.2
Step-by-step explanation:
find the extreme values of [tex]f(x,y) =x^{2} +y^2\\[/tex]
The function f(x,y) = x² + y² has a minimum value of 0 at the point (0,0) and has no maximum value.
What is a function?
A function is a relation between a set of inputs and a set of possible outputs, with the property that each input is related to exactly one output.
The function f(x,y) = x² + y² represents the sum of the squares of the variables x and y. To find the extreme values of this function, we need to take the partial derivatives with respect to x and y and set them equal to zero.
∂f/∂x = 2x = 0
∂f/∂y = 2y = 0
From these equations, we can see that the critical point occurs at (x,y) = (0,0).
To determine whether this is the maximum or minimum, we can use the second partial derivative test. The second partial derivatives are:
∂²f/∂x² = 2
∂²f/∂y² = 2
∂²f/∂x∂y = 0
At (0,0), ∂²f/∂x² > 0 and ∂²f/∂y² > 0, so the critical point is a minimum.
Therefore, the function f(x,y) = x² + y² has a minimum value of 0 at the point (0,0) and has no maximum value.
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The electrical signal created by a piece of test equipment at a specific point in time is described by the function v inst(t)=12xsin(360x60x6.3+79). What is the maximum voltage produced by the system?
The maximum voltage produced by the system is 12 volts.
The function given is:
[tex]v_{inst}(t) = 12 * sin(360 * 60 * 6.3 + 79)[/tex]
To find the maximum voltage produced by the system, we need to determine the maximum value of the sine function within the given range.
Let's focus on the argument of the sine function: 360 * 60 * 6.3 + 79.
First, calculate the value of the argument:
360 * 60 * 6.3 + 79 = 136080 + 79 = 136159
Now, substitute this value back into the sine function:
sin(136159)
The sine function has a periodicity of 360 degrees or [tex]2\pi[/tex] radians. Therefore, we can subtract multiples of 360 degrees from the argument without changing the value of the sine function. Let's find the nearest multiple of 360 degrees to 136159:
136159 ÷ 360 [tex]^\sim_\sim[/tex] 378.22
Since the quotient is not an integer, we can conclude that subtracting multiples of 360 degrees will not bring us closer to a maximum or minimum value of the sine function.
Therefore, to find the maximum voltage, we need to evaluate sin(136159) directly. However, calculating the sine function of such a large number is not practical or necessary. The sine function oscillates between -1 and 1, and the maximum value it can reach is 1.
So, regardless of the specific value of sin(136159), the maximum voltage produced by the system will be:
Maximum voltage = 12 * 1 = 12 volts.
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Make x the subject of the formula where x is positive:
2(x-2y) = 6xz+5u
Answer:
x = [tex]\frac{5u+4y}{2-6z}[/tex]
Step-by-step explanation:
2(x - 2y) = 6xz + 5u ← distribute parenthesis on left side
2x - 4y = 6xz + 5u ( add 4y to both sides )
2x = 6xz + 5u + 4y ( subtract 6xz from both sides )
2x - 6xz = 5u + 4y ← factor out x from each term on the left side
x(2 - 6z) = 5u + 4y ← divide both sides by (2 - 6z)
x = [tex]\frac{5u+4y}{2-6z}[/tex]
Between 2000 and 2015, the number of twin births in a certain country increased by 14%, to approximately 133,950 . About how many twin births were there in 2000? There were approximately ____ twin births in 2000.
Let the number of twin births in 2000 be x.
According to the problem, the number of twin births in 2015 increased by 14%, which means the number of twin births in 2015 is:
x + 0.14x = 1.14x
We also know that the number of twin births in 2015 is approximately 133,950, so we can set up the following equation:
1.14x = 133,950
Solving for x, we get:
x = 117,500
Therefore, there were approximately 117,500 twin births in 2000.
What inequality matches this graph?
A. x > -5
B. x > -5
C. x < -5
D. x < -5
Answer:
x ≥ -5
Step-by-step explanation:
Since we see the dot is filled in, we know the sign is either ≤ or ≥. Then, we can see that x is greater than -5 as the arrow is pointing in the positive direction (to the right). Therefore, it would be x ≥ -5
A certain drug is used to treat asthma. In a clinical trial of the drug, 30 of 298 treated subjects experienced headaches (based on data from the manufacturer). The accompanying calculator display shows results from a test of the claim that less than 9% of treated subjects experienced headaches. Use the normal distribution as an approximation to the binomial distribution and assume a 0.01 significance level to complete parts (a) through (e) below.
1-PropZTest
prop<0.09
z=0.643690407
p=0.7401118941
p=0.1006711409
n=298
Question content area bottom
Part 1
a. Is the test two-tailed, left-tailed, or right-tailed?
Right tailed test
Two-tailed test
Left-tailed test
Part 2
b. What is the test statistic?
z=enter your response here
(Round to two decimal places as needed.)
Part 3
c. What is the P-value?
P-value=enter your response here
(Round to four decimal places as needed.)
Part 4
d. What is the null hypothesis, and what do you conclude about it?
Identify the null hypothesis.
A.Upper H 0 : p greater than 0.09
H0: p>0.09
B.Upper H 0 : p less than 0.09
H0: p<0.09
C.Upper H 0 : p not equals 0.09
H0: p≠0.09
D.Upper H 0 : p equals 0.09
H0: p=0.09
Part 5
Decide whether to reject the null hypothesis. Choose the correct answer below.
A.
Fail to reject the null hypothesis because the P-value is greater than the significance level, α.
B.
Fail to reject the null hypothesis because the P-value is less than or equal to the significance level, α.
C.
Reject the null hypothesis because the P-value is less than or equal to the significance level, α.
D.
Reject the null hypothesis because the P-value is greater than the significance level, α.
Part 6
e. What is the final conclusion?
A.
There is not sufficient evidence to support the claim that less than 9% of treated subjects experienced headaches.
B.
There is sufficient evidence to warrant rejection of the claim that less than 9% of treated subjects experienced headaches.
C.
There is sufficient evidence to support the claim that less than 9% of treated subjects experienced headaches.
D.
There is not sufficient evidence to warrant rejection of the claim that less than 9% of treated subjects experienced headaches.
For the drug used to treat asthma in a clinical trial:
a) A, right-tailedb) 0.64c) 0.7401d) A, p > 0.09A, Fail to reject the null hypothesise) DHow to determine hypothesis?Part 1:
The test is right-tailed because the alternative hypothesis is that less than 9% of treated subjects experienced headaches.
Part 2:
The test statistic is z = 0.64, rounded to two decimal places (given in the calculator display).
Part 3:
The P-value is 0.7401, rounded to four decimal places (also given in the calculator display).
Part 4:
The null hypothesis is Upper H₀: p ≥ 0.09. We conclude that there is not sufficient evidence to support the claim that less than 9% of treated subjects experienced headaches.
Part 5:
We fail to reject the null hypothesis because the P-value is greater than the significance level, α=0.01.
Part 6:
The final conclusion is: D, There is not sufficient evidence to support the claim that less than 9% of treated subjects experienced headaches.
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Which of these shapes have rectangular cross sections options. Orectangular prism O triangular prism cylinder D cone ✔cy Osquare pyramid triangular pyramid
The correct options are rectangular prism, square pyramid.
What are the shapes have rectangular cross sections?When a shape has a rectangular cross-section, it means that if the shape is cut perpendicular to its base, the resulting cut will be a rectangle. So, the only shapes that will have a rectangular cross section are those whose base is a rectangle or a shape that can be inscribed within a rectangle.
The shapes that have rectangular cross sections when they are cut perpendicular to the base are:
Rectangular prism
Square pyramid
Therefore, the correct options are rectangular prism, square pyramid.
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Complete question:
a country radio station wants to know what the most popular type of music is so they ask their listeners to call in say their favorite type
According to the information, if the radio selects listerners randomly, the sample is random. But if they select listerners are selected without random method the sample may be biased.
Is this an example of sample random or not?If the radio station randomly selected a subset of their listeners and asked them to call in, then the sample would be random. This would help ensure that the sample is representative of the overall population of the radio station's listeners, and would allow for valid conclusions to be drawn about the preferences of the wider population based on the results of the survey.
However, if the radio station did not use a random sampling method, then the sample may be biased and not representative of the overall population of the radio station's listeners. For example, if the radio station only advertised the survey during certain times of day or on certain shows, then the sample may be biased towards listeners who are more likely to be listening during those times or shows. Similarly, if the radio station only advertised the survey on certain social media platforms or websites, then the sample may be biased towards listeners who use those platforms or websites.
Note: This question is incomplete. Here is the complete information:
State whether or not the sample is random. If it is not random, explain why
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What kind of geometric transformation is shown in the line of music?
•
reflection
translation
glide reflection
7 boxes of hamburger weighs 227 lb 8 az
(Simplify your answer)
Supermarket Chain A ships hamburger meat by placing 10 packages of hamburger in a box, with each package weighing 3 lb 4 oz. How much will 7 boxes of hamburger weigh?
Answer: each package weighs 3.25lb
Step-by-step explanation:
looking at the weight of each package (3lb 4oz), we can convert the 4oz to pounds by dividing by 16oz/lb; 4/16 = 0.25lb
Erica spins a spinner with equal sections numbered 1 through 4 and selects a colored tile from a bag. Based on the tree diagram given, what is the probability of spinning a 2 or 3 on the spinner and drawing a blue tile?
Therefore, the probability of spinning a 2 or 3 on the spinner and drawing a blue tile is 1/6.
What is probability?Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible, and 1 indicating that the event is certain to occur. Probability theory is an important branch of mathematics used in many fields, including statistics, economics, engineering, and science, to help make predictions and informed decisions based on data and uncertain events.
Here,
Based on the given tree diagram, the probability of spinning a 2 or 3 on the spinner is 1/2 since there are two possible outcomes (2 or 3) out of four equally likely outcomes (1, 2, 3, or 4).
The probability of drawing a blue tile after spinning a 2 or 3 is 1/3 since there is only one blue tile out of three possible outcomes (blue, green, or red) for each spin result of 2 or 3.
To calculate the probability of both events happening together (spinning a 2 or 3 and drawing a blue tile), we need to multiply the two probabilities:
P(2 or 3 and blue) = P(2 or 3) x P(blue | 2 or 3)
= (1/2) x (1/3)
= 1/6
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Question 1 of 10
The function f(x) is shown in this graph.
The function g(x) = -2x - 5.
Compare the slopes and y-intercepts.
A. The slopes are the same but the y - intercepts are different.
What is a slope in a graph?In a graph, the slope is the steepness of a line, which is a measure of how quickly the y-coordinate changes with respect to the x-coordinate. It is represented by the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line.
The slope is often denoted by the letter m, and is calculated as:
m = (y₂ - y₁) / (x₂ - x₁)
where (x₁, y₁) and (x₂, y₂) are any two points on the line.
What is Y-intercept in a graph?In a graph, the y-intercept is the point where a line or curve intersects the y-axis. It is the value of the dependent variable (usually denoted by y) when the independent variable (usually denoted by x) is equal to zero.
The y-intercept is often denoted by the letter b, and is expressed as a coordinate point (0, b), where 0 represents the x-coordinate and b represents the y-coordinate. For example, in the equation of a line y = mx + b, the y-intercept is the value of b.
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Find the circumference and area of the circle.
Answer:
9.38
Step-by-step explanation:
I did the math
The length of circumference of this circle is 21.9911 inches.
The area of this circle is, approximately, 38.4845 (in²).
Step-by-step explanation:For the circumference.1. Formula.The circumference of the circle can be easily found by utilizing the "π" (pi) number.This number is one of the most recognizible and emblematic numbers in math because it's the value of the ratio between any circle's length of circumference to it's diameter. Therefore, another way to express π is:
[tex]\sf \pi =\dfrac{s}{d}[/tex], where "s" is the length of the circumference of a circle, and "d" is the diameter of that same circle.
The value of π is not a variable, it is a constant for all circles, and it's, approximately, 3.141592653589793238... But don't worry, majority of calculator, if not all of them, have a button with the π so you can just click on it and have that value written automatically.
Fun fact: This number doesn't really have an end for its decimal figures because it's irrational.
2. Rewrite the formula.So now, taking the equation of π presented previously, we can rewrite the equation by solving it for "s", which is our variable of interest for this first parth. This is the process of that rewritting:
[tex]\sf \pi(d) =\dfrac{s}{d}(d)\\ \\\\\pi(d) =s\\ \\ \\s=\pi(d)[/tex]
3. Calculate.We're given the diameter of this circle, which is 7 inches. Now, substitute letter "d" on the formula by "7 inches" and calculate:
[tex]\sf s=\pi(7(in))=\boxed{\sf 21.9911(in)}.[/tex].
Remember that π is an irrational number, so any calculation involving it will result in an irrational answer aswell, unless the π is cancelled by another π.
The length of circumference of this circle is 21.9911 inches.
-------------------------------------------------------------------------------------------------------
For the area.1. Formula.These are the most commonly used formulas for the area of circles:
[tex]\sf1) A=\pi r^{2}[/tex]; where "r" is the radius of the circle.
[tex]\sf2) A=\dfrac{\pi d^{2}}{4}[/tex]; where "d" si the diameter of the circle.
Remember that the difference between the radius and diameter is just that the radius is half of the diamaterer. So, technically, everytime you have either the diameter of the radius, you can get both of the parameters.
2. Calculate.Let's use the area formula that directly involves diameter to avoid any conversions.
Substitute letter "d" by the length of the diameter (7 inches).
[tex]\sf A=\dfrac{\pi d^{2}}{4}=\dfrac{\pi (7(in))^{2}}{4}=\pi \dfrac{49}{4} (in^{2} )=\boxed{\sf 38.4845(in^{2} )}.[/tex]
Therefore, the area of this circle is, approximately, 38.4845 (in²).
-------------------------------------------------------------------------------------------------------
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Please help!!
If someone could explain how to solve this question I would appreciate it!
2430+15√2=
Answer: The given expression, 2430 + 15√2, cannot be simplified further as it is already in its simplest form. However, you can approximate its value using a calculator or by using a decimal approximation of the square root of 2.
Using a calculator, you can directly evaluate the expression to get:
2430 + 15√2 ≈ 2462.11
Alternatively, you can use a decimal approximation of the square root of 2, which is approximately 1.414:
2430 + 15√2 = 2430 + 15 * 1.414 ≈ 2430 + 21.21 = 2451.21
Therefore, 2430 + 15√2 is approximately equal to 2462.11 or 2451.21, depending on the method used for approximation.
Step-by-step explanation:
What kind of geometric transformation is shown in the line of music?
•
reflection
translation
glide reflection
Answer:
translation
hope this helps:) !!
Anita’s and Casey’s bills do not vary from month to month. Anita pays $80 more than Casey does each month. Over the course of 4 months, their combined bills are $1,520.
Part A
Write the system of equations that describes this situation. Let a represent Anita's monthly payment and c represent Casey's monthly payment.
a +
c =
a =
+
Part B
Solve the system to find Anita’s and Casey’s monthly payments.
Anita: $
Casey: $
Answer:
Casey's monthly payment is $150.
Anita's monthly payment is $230.
Step-by-step explanation:
Part A:
The system of equations that describes this situation is:
a + c = Total monthly bill
a = c + 80
where a represents Anita's monthly payment, c represents Casey's monthly payment, and Total monthly bill represents the combined bills of Anita and Casey.
Part B:
To solve the system, we can substitute the second equation into the first equation and get:
(c + 80) + c = Total monthly bill
Simplifying this equation, we get:
2c + 80 = Total monthly bill
We also know that over the course of 4 months, their combined bills are $1,520. So we can write:
4(Total monthly bill) = 1520
Substituting the equation for Total monthly bill from the previous step, we get:
4(2c + 80) = 1520
Simplifying this equation, we get:
8c + 320 = 1520
Subtracting 320 from both sides, we get:
8c = 1200
Dividing both sides by 8, we get:
c = 150
So Casey's monthly payment is $150. To find Anita's monthly payment, we can use the second equation from Part A:
a = c + 80
a = 150 + 80
a = 230
Therefore, Anita's monthly payment is $230.
tamara. Find the sum of two number cubes rolled at the same time. The chart below shows all possible sums from 36 possible combinations how many times should tamara expect the sum of two cubes to be equal to five if she rolls the cubes 180 times
Answer:
Step-by-step explanation:
There are 6 possible outcomes when rolling a single cube (1, 2, 3, 4, 5, or 6). When rolling two cubes, the possible sums range from 2 (1+1) to 12 (6+6). Using the chart provided, we can see that the sum of two cubes being equal to 5 only occurs once in the 36 possible combinations: when one cube shows a 1 and the other cube shows a 4.
To find the expected number of times this sum will occur if Tamara rolls the cubes 180 times, we need to multiply the probability of this event occurring on any given roll by the number of rolls. The probability of rolling a sum of 5 is 1/36, since there is only one way to get a sum of 5 out of the 36 possible combinations. Therefore, the expected number of times this sum will occur in 180 rolls is:
(1/36) x 180 = 5
So Tamara should expect to roll a sum of 5 about 5 times in 180 rolls of two cubes.
Hi can someone please help me out and explain the question in the picture? Thanks I appreciate it. I’ll give brainly :)
Answer:
$52.50
Step-by-step explanation:
1500 * 3.5% = 52.50
Answer:
$52.5 for the first year
Step-by-step explanation:
You can derive a decimal from a percentage by dividing by 100.
For example, 1% is 0.01
3.5% is 0.035
You can also move the decimal point back 2 places, but that's cringy.
So the problem says how much interest she will have to pay after one year, when the interest rate is 3.5%.
Therfore, we must multiply:
1500 by 3.5%
We stated that 3.5% is 0.035, so we can replace that
1500 * 0.035
Plug that into a caluclator and we get.....
$52.5 for the first year
ANSWER CHOICE 1
Phew! That was a long problem! May I please have Brainliest?
What is the discriminant of the quadratic equation − � 2 − 9 � − 8 = 0 −x 2 −9x−8=0?
we know that
discriminant of quadratic is [tex]b^{2}[/tex]-4ac
putting values we get
81-32
= 49
hence the discriminant is 49
y = x² - 6x +9
y = -x² +17
The quadratic equation is solved and intersect at the points (4, 1) and (-1, 16)
Given data ,
To find the intersection points of the two functions, we can set them equal to each other and solve for x:
x² - 6x + 9 = -x² + 17
Bringing all the terms to one side:
2x² - 6x - 8 = 0
Dividing by 2:
x² - 3x - 4 = 0
We can factor this quadratic equation as:
(x - 4)(x + 1) = 0
So the solutions are:
x = 4 or x = -1
To find the corresponding values of y, we can substitute each value of x into either of the original equations
y = x² - 6x + 9
When x = 4:
y = 4² - 6(4) + 9 = 1
So one intersection point is (4, 1).
When x = -1:
y = (-1)² - 6(-1) + 9 = 16
So the other intersection point is (-1, 16).
Hence , the two functions intersect at the points (4, 1) and (-1, 16)
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A single fair dice is rolled. Find the probability of getting a 2?
Answer:
1/6
Step-by-step explanation:
Chances of getting 2 = 1/6
in how many months will $8500 grow to $8818.75 at 5% P.A?
Is this compound interest or simple interest? I'll just do it by the simple interest method. The answer is 9 months!
What is the correct answer for 17? Plsss help
If lines m and n are parallel, then the value of x must be 4.
How to find the value of x?
If lines m and n are parallel, then the measures of the angles in the correspondent quadrants must be the same ones.
Here we can see that the two angles are in the third quadrant, thus, these angles have the same measure. Then we can write this as:
6x² = 96
Now we can solve this for x, we will get:
x² = 96/6
x² = 16
x = √16
x = 4
That is the value of 4.
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This is ixl olease help
Answer:
m<H = 62.7°
Step-by-step explanation:
If we use an inverse sin, then that would be sin^-1(8/9) Because Sin equals opposite over adjacent.
Answer:
H = 62.7 degrees
Step-by-step explanation:
Because this is a right triangle, we can use one of the trigonometric functions to find angle H:
Notice that sides HJ and IJ are given. If we are trying to find angle H, then HJ is the hypotenuse (longest side) and IJ is the opposite (side opposite to the angle we are trying to find). Since the opposite and hypotenuse are both given, we can use a sine function to find the angle of H (keep in mind that sin(<) = opp/hyp):
sin(H) = 8/9
We have to use the inverse of sine (sin^-1 or arcsin) to find angle H and use a calculator to solve:
arcsin(8/9) = H = 62.7 degrees
If 90% of a number is 110, find 9% of that number.
We can set up the equation :
0.9x = 110 ,
where x is the unknown number. To solve for x, we can divide both sides by 0.9 :
x = 110 ÷ 0.9
x = 122.22 (rounded to two decimal places)
So the unknown number is approximately 122.22.
To find 9% of that number, we can multiply 122.22 by 0.09 :
0.09 × 122.22 = 11.00 (rounded to two decimal places)
Therefore, 9% of the number is approximately 11.
2 1/2 - 4 1/4
how do I slove this
The fraction expression 2 1/2 - 4 1/4 when evaluated is -1 3/4
Evaluating the fraction expressionTo solve 2 1/2 - 4 1/4, we need to convert the mixed numbers into improper fractions, then find a common denominator and subtract the two fractions.
First, we convert 2 1/2 and 4 1/4 into improper fractions:
2 1/2 = 5/2
4 1/4 = 17/4
Next, we find a common denominator. In this case, the smallest common denominator is 4:
5/2 = 10/4
17/4 = 17/4
Now we can subtract the fractions:
10/4 - 17/4 = -7/4
Finally, we can convert the resulting improper fraction back into a mixed number:
-7/4 = -1 3/4
Therefore, 2 1/2 - 4 1/4 = -1 3/4.
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50 Points! Multiple choice algebra question. Photo attached. Which represents the correct synthetic division of (x^2-4x+7) divided by (x-2)? Thank you!
Option D is the correct synthetic division of (x^2-4x+7) divided by (x-2)
What is the synthetic division?Synthetic division is a shorthand procedure used to divide a polynomial by a linear factor of (x - a) form, in which "a" is constant. This method gives an expedient way to locate the quotient and remainder without carrying out long division.
x - 2 | x^2 - 4x + 7
x^2 - 2x
---------
-2x + 7
-2x + 4
-------
3
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sin negative-1 (-3sqrt/2) in radians
The given trigonometric expression sin⁻¹(-3√(2)/2) in radians is approximately -2.2143 radians.
As we know that sin⁻¹(x) = -cos⁻¹(x) + π/2, which is the angle in the fourth quadrant whose cosine is 3sqrt(2)/2.
We have:
cos²θ + sin²θ = 1
Since sine is negative and cosine is positive, we know that:
sinθ = -sqrt(1 - cos²θ)
Substituting cosθ = 3√(2)/2, we get:
sinθ = -√(1 - (3√(2)/2)²) = -√(1 - 9/8) = -√(1/8) = -√(2)/2
Therefore, sin^(-1)(-3sqrt(2)/2) = -cos^(-1)(3sqrt(2)/2) + π/2.
Since cosine is positive in the fourth quadrant, we have:
cos⁻¹(3√(2)/2) = π/4
Substituting this value, we get:
sin⁻¹(-3√(2)/2) = -π/4 + π/2 = π/4
Therefore, sin⁻¹(-3√(2)/2) in radians is approximately -2.2143 radians.
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Anyone know how to find the radius when given this?
Answer:
The radius is 26 units--------------------------
As per given, the distance from the center to both of the chords is same, therefore both chords have same length:
JK = ML4x = 6x - 246x - 4x = 242x = 24x = 12The length of each chord is:
4*12 = 48 unitsUse Pythagorean theorem to find the radius, the distance from the center to one end of the chord:
[tex]QM=\sqrt{QP^2+MP^2}[/tex][tex]QM=\sqrt{10^2+(48/2)^2}=\sqrt{100+576}=\sqrt{676} =26\ units[/tex]The mayor of a town has proposed a plan for the construction of a new bridge. A political study took a sample of 800 voters in the town and found that 53% of the residents favored construction. Using the data, a political strategist wants to test the claim that the percentage of residents who favor construction is more than 49%. Find the value of the test statistic. Round your answer to two decimal places.
the value of the test statistic is approximately 5.19.we can get the answer by using formula .
what is statistic ?
A statistic is a numerical value or measure that is calculated from a sample of data, and is used to describe or make inferences about a population. Statistics are used in various fields, including business, economics, social sciences, and natural sciences, to analyze data
In the given question,
To test the claim that the percentage of residents who favor construction is more than 49%, we can use a one-sample z-test. The test statistic can be calculated as:
z = (p - P) / √(P * (1 - P) / n)
where:
p = the sample proportion (0.53)
P = the hypothesized population proportion under the null hypothesis (0.49)
n = the sample size (800)
Substituting the given values into the formula, we get:
z = (0.53 - 0.49) / √(0.49 * 0.51 / 800) ≈ 5.19
Rounding the test statistic to two decimal places, we get:
z ≈ 5.19
Therefore, the value of the test statistic is approximately 5.19.
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