Answer:
Lower limit: 11.7 cm
Upper limit: 16.263
Explanation:
The formula to find the lower and upper limits of the confidence interval (given the data is normally distributed) is :
[tex]CI=\mu\pm Z^*\frac{\sigma}{\sqrt{n}}[/tex]Where:
• μ = sample mean
,• σ = sample standard deviation
,• Z* = critical value of the z-distribution
,• n = is the sample size
In this case:
• μ = 14cm
• σ = 4cm
,• n = 12
The critical value of the z-distribution for a confidence interval of 95% is Z* = 1.96
Now, we can use the formula above to find the upper and lower limit:
[tex]CI=14\pm1.96\cdot\frac{4}{\sqrt{12}}=14\pm\frac{98\sqrt{3}}{75}=\frac{1050\pm98\sqrt{3}}{75}[/tex]Thus:
[tex]Lower\text{ }limit=\frac{1050-98\sqrt{3}}{75}\approx11.736cm[/tex][tex]Upper\text{ }limit=\frac{1050-98\sqrt{3}}{75}\approx16.263cm[/tex]Rounded to one decimal:
Lower limit: 11.7cm
Upper limit: 16.3cm
he center of the circle below is at P. If arc AB measures 86 °, then what is the measure of the angle < APB ?
Answer:
D. 86°
Explanation:
Given:
• The center of the circle = P
,• The measure of arc AB = 86°
We want to find the measure of the angle APB.
By Circle's theorem: The measure of an arc is equal to the measure of the central angle subtended by the same arc.
Applying this theorem, we have that:
[tex]\begin{gathered} m\angle APB=m\widehat{AB} \\ \implies m\angle APB=86\degree \end{gathered}[/tex]The measure of the angle APB is 86 degrees.
Option D is correct.
Hello, I need help completing this math problem. I will include a picture. Thank you so much!
From the given picture, we can see that the figure is a right triangle, so we can apply Pythagorean theorem, that is,
[tex]5^2+8^2=x^2[/tex]where x denotes the missing length. Then, our equation give us
[tex]\begin{gathered} x^2=25+64 \\ x^2=89 \end{gathered}[/tex]By taking square root to both side, we have
[tex]\begin{gathered} x=\sqrt[]{89} \\ x=9.4339 \end{gathered}[/tex]Therefore, by rounding this result to the nearest tenth, the answer is 9.4 ft
X Y2 146 4211 77Find the constant of proportionality (r) in the equation y=rx.
From the question
We are given the equation
[tex]y=rx[/tex]We are to find r given that
When x = 2, y = 14
When x = 6, y = 42
When x = 11, y = 77
Substituting the first value, x = 2, y = 14 into the equation we get
[tex]14=r\times2[/tex]Solving for r we get
[tex]\begin{gathered} r=\frac{14}{2} \\ r=7 \end{gathered}[/tex]This is true for all values of x and y
Hence, r
PLEASE HELP ASAP! What is the standard form of the hyperbola that the receiver sits on if the transmitters behave as foci of the hyperbola?
A hyperbola is a particular kind of smooth curve that lies in a plane and is classified by its geometric characteristics or by equations for which it is the solution set.
What is hyperbola?A hyperbola is a particular kind of smooth curve that lies in a plane and is classified by its geometric characteristics or by equations for which it is the solution set. A hyperbola is made up of two mirror images of one another that resemble two infinite bows.These two sections are known as connected components or branches. A series of points in a plane that are equally spaced out from a directrix or focus is known as parabolas. The difference in distances between a group of points that are situated in a plane and two fixed points—which is a positive constant—is what is referred to as the hyperbola.Therefore, a hyperbola is a particular kind of smooth curve that lies in a plane and is classified by its geometric characteristics or by equations for which it is the solution set.
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The diameter of the Milky Way is 2 x 10²⁰ meters. The radius of Earth is 6.37 x 10⁶meters. About how many times as great is the diameter of the Milky Way than the radius of Earth? The diameter of the Milky Way is about
Answers: 4.37 X 10¹⁴
3.1 X 10¹⁴
4.37 X 10¹³
3.1 X 10¹³
(blank) times as great as the radius of Earth.
Answer:
3.1 x [tex]10^{13}[/tex]
Step-by-step explanation:
[tex]\frac{2x10^{20} }{6.37x10^{6} }[/tex]
3/6.37 is about .31
When you are dividing with powers, you subtract the exponents
20 - 6 = 14
.31 x [tex]10^{14}[/tex] This is not in scientific notation because .31 is less than 1
3.1 x [tex]10^{-1}[/tex]x[tex]10^{14}[/tex] When we multiply powers with the same base we add the exponents
3.1 x [tex]10^{13}[/tex]
Write the product using exponents. I need help I’m not sure how to do this
Given:
The given expression is,
[tex]\frac{1}{5}\cdot\frac{1}{5}\cdot\frac{1}{5}\cdot\frac{1}{5}\cdot\frac{1}{5}[/tex]Required:
Write the product using exponent.
Answer:
Let us compute the product using exponents.
[tex]\begin{gathered} \frac{1}{5}\cdot\frac{1}{5}\cdot\frac{1}{5}\cdot\frac{1}{5}\cdot\frac{1}{5} \\ =(\frac{1}{5})^5 \\ =\frac{\left(1\right)^5}{\left(5\right)^5} \\ =\frac{1}{3125} \end{gathered}[/tex]Final Answer:
The product using exponents is given by,
[tex]\frac{1}{3125}[/tex]
Sean, Kevin and Bill take classes at both JJC and CSU. Sean takes 8 credits at JJC and 4 credits at CSU; Kevin takes 10 credits at JJC and 6 at CSU: Bill takes 6 credits at JJC and 4 at CSU; the cost per credit at JJC is $103 and at CSU is $249. a) Write a matrix A that gives the credits each student is taking and B that gives the cost per credit at each school. b) Find the dimension of A and B. c) Find the product AB and the names of its rows and columns.
ANSWER:
a)
[tex]\begin{gathered} A=\begin{pmatrix}8 & 4 \\ 10 & 6 \\ 6 & 4\end{pmatrix} \\ B=\begin{pmatrix}103 \\ 249\end{pmatrix} \end{gathered}[/tex]b)
Dimension A = 3 x 2
Dimension B = 2 x 1
c)
Cost of credits
Sean $1820
Kevin $2524
Bill $1614
[tex]\begin{pmatrix}Sean \\ \: Kevin \\ \: Bill\end{pmatrix}\begin{pmatrix}1820 \\ \: 2524 \\ \: 1614\end{pmatrix}[/tex]STEP-BY-STEP EXPLANATION:
With the help of the statement, we create the matrices A and B:
[tex]\begin{gathered} A=\begin{pmatrix}8 & 4 \\ 10 & 6 \\ 6 & 4\end{pmatrix}\rightarrow3\times2 \\ B=\begin{pmatrix}103 \\ 249\end{pmatrix}\rightarrow2\times1 \end{gathered}[/tex]Now, we calculate the product just like this:
[tex]\begin{gathered} \text{Product }A\cdot B=\begin{pmatrix}8\cdot103+4\cdot249 \\ 10\cdot103+6\cdot249 \\ 6\cdot103+4\cdot249\end{pmatrix}=\begin{pmatrix}1820 \\ \: 2524 \\ \: 1614\end{pmatrix} \\ \text{Product }A\cdot B=\begin{pmatrix}Sean \\ Kevin \\ Bill\end{pmatrix}\begin{pmatrix}1820 \\ 2524 \\ 1614\end{pmatrix} \end{gathered}[/tex]Use the Pythagorean Theorem to find x, in simplest radical form. 20
The Pythagorean theorem states that the sum of the squares of the two sides of a right angle is equal to the square of the hypotenuse (longest side).
[tex]\begin{gathered} a^2+b^2=c^2 \\ \text{where }c\text{ is the hypotenuse, and }a\text{ and }b\text{ are the other two sides of a right triangle.} \end{gathered}[/tex]Given: c = 20, a = 8, and b = x. Find x.
[tex]\begin{gathered} a^2+b^2=c^2 \\ (8)^2+(x)^2=(20)^2 \\ 8^2+x^2=20^2^{} \\ 64+x^2=400 \\ x^2=400-64 \\ x^2=336 \\ \sqrt{x^2}=\sqrt[]{336} \\ x=\sqrt[]{16\cdot21} \\ x=4\sqrt{21}\text{ (final answer)} \end{gathered}[/tex]I need help, I did 1-2b, but i do not mind someone answering it either way so I can double check, but I am mainly stuck with 2c and if someone can tell me the answer and as to why, it would mean a lot and you can get brainlest if it is the right answer :)(Not a multiple choice question)
Absolute Minimum: an absolute minimum point is a point where the function obtains its least possible value.
The given function :
[tex]f(x)=x^4-4x^3-x^2+12x-2[/tex]In the graph of the f(x) , the least value of x of the given curve is : (-0.939)
and the f(x) at x = (-0.939) is -10.065
The absolute minimum value is (x,y) = (-0.939, -10.065)
To round off in the nearest hundredth : (x, y) = (-0.94, -10.07)
Answer : (x, y) = (-0.94, -10.07)
The point P is on the unit circle. If the y-coordinate of P is −3/5, and P is in quadrant IV, then
x = _________
Answer:
[tex]\frac{4}{5}[/tex]
Step-by-step explanation:
Knowing that [tex]{-\frac{3}{5}}^{2} + {\frac{4}{5}}^{2} = 1, {-\frac{3}{5}}^{2} + {-\frac{4}{5}}^{2} = 1[/tex],
so x can be positive or negative 4/5,
and we know that x coordinate of any point in quadrant IV is positive,
so x = 4/5.
3-35. Fisher thinks that any two lines must have a point of intersection. Is he correct? If so, explain how youknow. If not, produce a counterexample. That is, find two lines that do not have a point of intersection and explainhow you know
Any two lines must have a point of intersection, with ONLY ONE exception : when the lines are parallel. That means they have exactly the same inclination or Slope.
As an example of two lines that hasnt point of intersection they are
y = 5x + 16
y = 5x + 11
We know both lines have no point of intersection because
both have the same slope or inclination m. By comparation with slope intercept equation
y = mx + b
then we see both have same inclination, and b is 11 in one line and 16 in the other line. This means both lines are parallel with one line going over the other line, without touching it in any point.
Can someone help me with this math question. I just need to see the work.
pic of question below
The polar coordinates for each point are given as follows:
a. [tex](r, \theta) = \left(2\sqrt{5}, \frac{7\pi}{4}\right)[/tex]
b. [tex](r, \theta) = \left(6, \frac{\pi}{3}\right)[/tex]
Polar coordinatesSuppose we have a point with Cartesian coordinates given as follows:
(x,y).
The polar coordinates will be found as follows:
r² = x² + y².θ = arctan(y/x).For item a), the Cartesian coordinates are as follows:
(-4, 4).
Hence the polar coordinates will be given as follows:
r² = (-4)² + (4)² -:> r = sqrt(32) = 2sqrt(5).θ = arctan(-4/4) = arctan(-1) = -45º = 2pi - pi/4 = 7pi/4.For item a), the Cartesian coordinates are as follows:
(3, 3sqrt(3)).
Hence the polar coordinates will be given as follows:
r² = (3)² + (3sqrt(3))² = 9 + 27 = 36 -> r = sqrt(36) = 6.θ = arctan(3sqrt(3)/3) = arctan(sqrt(3)) = 60º = pi/3.More can be learned about polar coordinates at https://brainly.com/question/7009095
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Where are all the tutors at??? Like it won’t even let me ask a tutor
The scatter plot is given and objective is to find the best line of fit for given scatter plot.
Let's take the few points of scatter plot,
(0,8) ,( -1,8) , (-4,10) ,( -8,12),(-10,14) (-12,14)
Take the line and check which graph contains most of the points of scatter plot.
[tex]1)\text{ f(x)=}\frac{-1}{2}x+8[/tex]The graph is ,
now take ,
[tex]2)\text{ f(x)=x+8}[/tex]The graph is,
This graph contains only one point of scatter plot.
Take,
[tex]3)\text{ f(x)= 10}[/tex]Now the take the last equation,
[tex]4)\text{ f(x)=-2x+14}[/tex]this graph contains no point of the scatter plot.
From all the four graph of the lines it is observed that option 1) is the best line of fit for given scatter plot. because it contains 3 points of scatter plotes . which is more than the other graph of line.
Answer: Option 1)
Write an equation of variation to represent the situation and solve for the indicated information Wei received $55.35 in interest on the $1230 in her credit union account. If the interestvaries directly with the amount deposited, how much would Wei receive for the sameamount of time if she had $2000 in the account?
Determine whether the equation represents an exponential growth function, anexponential decay function, and give the percent growth or decay.17. y = 18(1.3)^t
A exponential growth or decay function has the next general form:
[tex]y=a(1\pm r)^t[/tex]If it is :
(1+r) , (>1) the function growth
(1-r) , (<1) the function decay
------
The given equation:
[tex]y=18(1.3)^t[/tex]As the (1+r) is equal to 1.3 (> 1) then it is a exponential growth function.In (1+r) the r is the percent of growth, then for the given equation you have:
[tex]\begin{gathered} 1+r=1.3 \\ r=1.3-1 \\ \\ r=0.3 \end{gathered}[/tex]The percent of decay is 0.3 or 30%The following are the annual salaries of 15 chief executive offers of major companies. The salaries are written in thousands of dollars.
The original data is:
405, 1108, 84, 315, 495, 609, 362, 428, 224, 338, 700, 790, 814, 767, 633
To find the required percentiles, we need to sort the dataset from lowest to highest.
84, 224, 315, 338, 362, 405, 428, 495, 609, 633, 700, 767, 790, 814, 1108
The total number of data is 15.
a) The 25th percentile is the element located at the position:
25/100 * 15 = 3.75
Rounding down, the position is 3, so the 25th perc
a rectangular rug has dimensions of 9'×12'find area of the rug
Explanation:
Area of the rectangular rug = length × width
dimension of rug = 9'×12'
length = 12', width = 9'
Area = 12 × 9
Area = 18
2,000 deposit,compound interest,compounded anually,at 6% for 2 years. What is the total balance(A=Principal+Interest)?
Given a principal P, compounded anually at r% for t years. Then the
the difference of twice h and 5 is as much as the sum of h and 4
The value of h by solving the given relationship we get, h = 9
In the above question, a word problem is given with the following relations which are as
First we'll express the given word problem statements into mathematical equation expressions
Therefore, The difference of twice of h and 5 is as much as the sum of h and 4
It can be written as in mathematical equation form as
2h - 5 = h + 4
Now, we need to find the value of h by solving the above mathematical equation formed put of the given relationship
Here,
2h - 5 = h + 4
2h - h = 5 + 4
h = 9
Hence, The value of h by solving the given relationship we get, h = 9
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What is the slope of the line in the graph?A. 1 B. 2C. 0 D. -2
Always remember that the slope is the number of units on the Y-axis in relation to the X movement.
A horizontal line always has a slope of 0. (it is not increasing in the Y-axis)
If the scale factor is 4, what is the measurement of x?24 m4 m20 m16 m
Let:
[tex]\begin{gathered} 6k=x \\ \end{gathered}[/tex]where:
k = scale factor
If the scale factor is 4, then:
[tex]\begin{gathered} 6(4)=x \\ 24=x \\ x=24 \end{gathered}[/tex]LanaCharles almn on the coordinate plane what is the perimeter of a ALMN round to the nearest unit
The Solution:
Given the graph below:
We are required to find the perimeter of the triangle LMN rounded to the nearest unit.
Step 1:
Find the distance LM, where L(-3,2) and M(3,5)
By the formula for distance between two points, we have
[tex]LM=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Where,
[tex]\begin{gathered} x_1=-3 \\ y_1=2 \\ x_2=3 \\ y_2=5 \end{gathered}[/tex]Substituting, we get
[tex]LM=\sqrt[]{(3--3)^2+(5-2)^2}=\text{ }\sqrt[]{6^2+7^2}=\text{ }\sqrt[]{85}=9.2195[/tex]Step 2:
Find the distance LN:
[tex]LN=12[/tex]Step 3:
Find the distance MN, where M(3,5) and N(9,2)
[tex]MN=\sqrt[]{(9-3)^2+(2-5)^2}=\text{ }\sqrt[]{6^2+(-3)^2}=\text{ }\sqrt[]{45}=6.7082[/tex]Step 4:
The perimeter is:
[tex]\text{ Perimeter=LM+MN+LN=9.2195+6.7082+12=27.9277}\approx28\text{ units}[/tex]Therefore, the correct answer is 28 units.
A)As the x-value Increases by one, the y-value decreases by 2.26.B)As the x-value increases by one, the y-value decreases by 53.769.C)As the x-value Increases by one, the y-value increases by 2.26.D)As the x-value Increases by one, the y-value Increases by 53.769. Which equation describes the line of best fit for the table below?
Option A
Explanations:The graph shows an inverse proportion.
As x increases, y decreases in value.
Finding the slope of the graph:
dy / dx = (y₂ - y₁) / (x₂ - x₁)
x₁ = 5, x₂ = 9, y₁ = 40, y₂ = 30
dy / dx = (30 - 40) / (9 - 5)
dy / dx = -10 / 4
dy / dx = -2.5
This means that as x increases by 1, decreases by 2.5
A is the only correct option.
Which statement is true about the relation shown on the graph below?
We know that a function has a unique value of y for each value in x so the correct statement is:
c. it is not a function because there are multiple y values for a given x value
i need help on number 7. Please use 4 points
In order to graph this equation, we need at least two points that are solution to the equation.
To find these points, we can choose values for x and then calculate the corresponding values of y.
Choosing the x-values of -2, -1, 0 and 1, we have:
[tex]\begin{gathered} x=-2\colon \\ y=-\frac{5}{2}\cdot(-2)-1 \\ y=5-1 \\ y=4 \\ \\ x=-1\colon \\ y=-\frac{5}{2}(-1)-1 \\ y=2.5-1 \\ y=1.5 \\ \\ x=0\colon \\ y=-\frac{5}{2}\cdot0-1 \\ y=-1 \\ \\ x=1\colon \\ y=-\frac{5}{2}\cdot1-1 \\ y=-2.5-1 \\ y=-3.5 \end{gathered}[/tex]So we have the points (-2, 4), (-1, 1.5), (0, -1) and (1, -3.5). Graphing these points and the line that passes through them, we have:
I need help IMMEDIATELY! I'm so confused and this is due in 7 minutes!!
I won't hesitate to give brainliest to whoever answers fastest! Please please please show work
1. Given [tex]f(x)= 2x^2-4x+2[/tex], what is the value of [tex]f(2/3)[/tex]?
2. Given [tex]f(x)= 4x^2+2x-6[/tex], what is the value of [tex]f(1/4)[/tex]?
The values of the functions are:
1. f(2/3) = 2/9
2. f(1/4) = -21/4
How to Find the Value of a Function?If we are given the a function to find the value for which x assumes a given value, substitute the given value of x into the function and solve.
1. To find the value of f(2/3), substitute x = 2/3 into the function f(x) = 2x² - 4x + 2.
f(2/3) = 2(2/3)² - 4(2/3) + 2
f(2/3) = 2(4/9) - 8/3 + 2
f(2/3) = 8/9 - 8/3 + 2
f(2/3) = (8 - 24 + 18)/9
f(2/3) = 2/9
2. To find the value of f(1/4), substitute x = 1/4 into the function f(x) = 4x² + 2x - 6.
f(1/4) = 4(1/4)² + 2(1/4) - 6
f(1/4) = 4(1/16) + 1/2 - 6
f(1/4) = 1/4 + 1/2 - 6
f(1/4) = (1 + 2 - 24)/4
f(1/4) = -21/4
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What is the slope and y-intercept?
y=3x-2
Options:
Blank # 1
Blank # 2
The value of slope is 3 and the value of y - intercept is -2.
Slope and y intercept:
The slope refers the rate of change in y per unit change in x.
The y-intercept states the y-value when the x-value is 0.
Given,
Here we have the equation
y = 3x - 2
Now, we need to find the slope and y intercept of the equation.
We know that, the standard form of the equation of the line is,
y = mx + b
Where
m represents the slope
b represents the y-intercept.
So, we have to rewrite the given equation as,
y = 3x + (-2)
So, while comparing the given equation with standard form, then we get,
the value of the slope is 3 and the value of the y intercept is -2.
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How many offices are between 41 and 50 meters ?
Solution
For this case we want to find the number of offices between 41 and 50 m and the answer is:
2 meters
The difference between the graph of a radical function and the graph of a rational function
The difference between the graph of a radical function and that of a rational function is:
A radical graph is drawn from a function that contains a root, it could be a square root, cube root, etc. Whenever you are graphing a radical function, we first need to consider the domain. Because of the square root sign, the domain and range are always restricted.
But a rational graph is drawn from the ratio of two polynomial functions where the function in the denominator is not equal to zero. A rational graph is characterized by asymptotes.
The major difference would be that a radical graph has a restricted domain due to the root, and usually without an asymptote, while a polynomial graph has a restricted domain and sometimes range which forms the asymptote (vertical, horizontal asymptote).
Please hurry!!!
Is there a relationship between the distance and the sum? Is there a relationship between the distance and the difference?
A 5-column table with 3 rows. Column 1 is labeled a with entries 1, 4, negative 6. Column 2 is labeled b with entries 2, negative 1, negative 3. Column 3 is labeled a + b with entries 3, 3, negative 9. Column 4 is labeled a minus b with entries negative 1, 5, negative 3. Column 5 is labeled Distance with entries 1 unit, 5 units, 3 units.
Which describes the relationship between the distance and the difference?
The distance is always the opposite of the difference.
The distance is exactly the difference.
The distance is the absolute value of the difference.
The distance is not related to difference.
The third option that is the distance is the absolute value of the difference describes the relationship between distance and difference.
We know that the distance between two points is the difference of those two values.
But as the distance between two points can never be negative, we will write the absolute value of the difference as the distance between the two points.
Here we can see that,
a - b = -1 when distance = 1
a - b = 5 when distance = 5
a - b = 3 when distance = 3
Hence, the relationship between difference and distance is described by the third option.
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