Hence,the area of circle [tex]=144\pi[/tex][tex]cm^{2}[/tex]
What is the circle?In a plane all points are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.
What is the area?The patch of size on a surface is determined by its area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, therefore the area of a plane area or .plane region refers to the area of a form of plane lamina .
we know that ,
area of circle =[tex]\pi r^{2}[/tex]
according to question,
r= 12 cm.
So,the area of circle
[tex]=\pi *12^{2} \\=\pi *144[/tex]
or the area of circle [tex]=144\pi[/tex][tex]cm^{2}[/tex]
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The bearing of A from B is 129 and the bearing of C from B is 219. If B is equidistant from A and C, find the bearing of C from A
The bearing of C from A is 90 degrees when B is equidistant from A and C.
What is bearing?In navigation and geometry, bearing refers to the direction or angle between two points, measured clockwise from a fixed reference direction. Typically, bearings are measured in degrees, with 0 degrees indicating a direction due north, 90 degrees indicating a direction due east, 180 degrees indicating a direction due south, and 270 degrees indicating a direction due west. Bearings can be expressed as either magnetic bearings or true bearings, depending on the reference direction used.
According to the given informationLet's assume that the distance from B to A and from B to C is the same.
To find the bearing of C from A, we can use the fact that the interior angles of a triangle sum up to 180 degrees. Therefore, we can first find the bearing of A from C:
180 - 129 = 51
This means that the bearing of C from A is 51 degrees in the opposite direction of the bearing of A from C. Since the bearing of A from C is 219, the bearing of C from A is:
219 - 180 + 51 = 90 degrees
Therefore, the bearing of C from A is 90 degrees.
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The line 2x+3y=-22 is tangent to a circle centered at (-1,2) What is the tangent point?
The point of tangency is (-3, -2).
How to find the intersection point?To find the point of tangency , we really want to find the convergence point between the line and the circle. We can begin by tracking down the situation of the circle with focus (- 1,2).
A circle's equation for its center (a,b) and radius (r) is as follows:
[tex](x - a)^2 + (y - b)^2 = r^2[/tex]
Plugging in the values for the center and solving for r, we get:
[tex](x + 1)^2 + (y - 2)^2 = r^2[/tex]
Now we need to find the intersection point between this circle and the line 2x+3y=-22. We can do this by substituting y = (-2/3)x - (22/3) into the equation of the circle:
[tex](x + 1)^2 + ((-2/3)x - (16/3))^2 = r^2[/tex]
Expanding and simplifying, we get:
[tex]10x^2 + 24x + 44 = 9r^2[/tex]
Next, we can make use of the fact that the line intersects the circle at a tangent. This indicates that the distance between the intersection point and the center of the circle is the same as its radius. The distance between the center of the circle and the line can be determined using the distance formula:
distance = [tex]|2x + 3y - (-22)\sqrt{2^2 + 3^2}| = |2x + 3y + 22| \sqrt(13)[/tex]
Setting this equal to the radius r, we get:
[tex]|2x + 3y + 22| \sqrt{13} = \sqrt{10x^2 + 24x + 44} / 3[/tex]
Squaring both sides and simplifying, we get:
[tex]36(2x + 3y + 22)^2 = 13(10x^2 + 24x + 44)[/tex]
Expanding and simplifying, we get:
[tex]26x^2 + 36xy + 45y^2 + 52x + 132y + 240 = 0[/tex]
Now we can use the quadratic formula to solve for x:
x = (-18y - 13 ± [tex]\sqrt{169 - 720y^2[/tex])) / 13
Substituting this into the equation for the line, we get:
2(-18y - 13 ± [tex]\sqrt{169 - 720y^2))[/tex] / 13 + 3y = -22
Simplifying, we get:
y = -2
Substituting y = -2 into the equation for x, we get:
x = -3
Therefore, the point of tangency is (-3, -2).
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The Olympic record for the men's 50-meter freestyle is 21.91 seconds. Express this speed in meters per second
Answer:
50 meters/21.91 seconds = 2.282 m/sec
Select each expression that is equivalent to 3(n + 6).
Answer:
3(n + 6) = 2(n + 6) + (n + 6)
3(n + 6) = 3n + 18
In art class students are mixing blue and red paint to make purple paint. Hawa mixes 1 cup of blue paint and 5 cups of red paint. Jacob mixes 4 cups of blue paint and 13 cups of red paint. Use Hawa and Jacob’s percent of red paint to determine whose purple paint will be redder.
Hawa percent of red paint (to nearest whole number) =
%
Jacob percent of red paint (to nearest whole number) =
%
Hawa ’s purple paint will be redder.
Jacob’s purple paint will be redder.
The two purple paints will be equally red.
attempt 1 out of 2
Miracle Jackson
Which is more? (Percent Comparison)
Apr 10, 6:51:14 PM
Watch help video
In art class students are mixing blue and red paint to make purple paint. Hawa mixes 1 cup of blue paint and 5 cups of red paint. Jacob mixes 4 cups of blue paint and 13 cups of red paint. Use Hawa and Jacob’s percent of red paint to determine whose purple paint will be redder.
Answer:
Step-by-step explanation:
A pre-image has coordinates N(3, -2), A(5, 0) and P(2, 4). The image has coordinates N’ (2, 0), A'(4, 2) and P'(1, 6). Write a transformation rule to describe the path the pre-image made to arrive at the image.
Answer:
f(x + 1) + 2
Step-by-step explanation:
All the points are translated 1 unit to the left and 2 units up.
To write a translation along the x-axis, movement to the right would be written as f(x - a), where a is the amount translated, and movement to the left would be written as f(x + a). In this case, we would need to write the translation as f(x + 1), since it is moving 1 unit to the left.
As for translations along the y-axis, movement upward would be written as f(x) + a, and movement downward would be written as f(x) - a. Thus, the transformation rule to describe the path the pre-image made to arrive at the image would be f(x + 1) + 2.
P.S. I'm a bit rusty with this stuff, so I apologize in advance if I messed something up.
tom can type a report in 3 hours and nelson takes 5 hours. how long will it take the two of them typing together?
It will take Tom and Nelson 1.875 hours, or 1 hour and 52.5 minutes, to complete the report working together.
How to know work done together?To solve this problem, we can use the concept of work done. Let's assume that a report is a unit of work, and Tom and Nelson each do a fraction of the work in one hour.
Tom can do the entire report in 3 hours, which means he can do 1/3 of the report in one hour. Similarly, Nelson can do 1/5 of the report in one hour.
If they work together, the fraction of the report they can do in one hour is the sum of their individual fractions:
1/3 + 1/5 = 8/15
So, together they can do 8/15 of the report in one hour. To find out how long it will take them to do the entire report working together, we can use the formula:
time = work ÷ rate
where work is 1 (the whole report) and rate is 8/15 (the fraction of the report they can do in one hour).
time = 1 ÷ (8/15)
time = 1.875 hours
Therefore, it will take Tom and Nelson 1.875 hours, or 1 hour and 52.5 minutes, to complete the report working together.
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Which statement is true? Please help
The statement that is equivalent to each other would be =
2×(4+2)-6 = 14÷(3.5×2)+4. That is option A.
What is equivalent equations?An equivalent equation is the type of equation that appears different but has the same answer when simplified or solved.
The first part;
=2×(4+2)-6
= 2×(6)-6
= 12-6 = 6
The second part;
= 14÷(3.5×2)+4
= 14÷7+4
= 2+4
= 6
Therefore, 2×(4+2)-6 = 14÷(3.5×2)+4. is a true statement.
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Here is a recipe for $$ cupcakes. • Terrance has $$ cup of flour and $$ eggs. • Duri has $$ cups of flour and $$ grams of butter. • Habib has $$ cups of milk and $$ cups of sugar. • Anika has $$ cup of sugar and $$ cups of milk. If each person has enough of all the other ingredients, how many cupcakes could they make on their own?
Duri can make 72 cupcakes on his own and Habib can make 36 cupcakes on her own, assuming they have enough of all the other ingredients.
To determine how many cupcakes each person can make on their own, we need to check if they have enough of all the other ingredients required to make 12 cupcakes.
Terrance has 1 cup of flour and 6 eggs, which is not enough to make 12 cupcakes.
Duri has 12 cups of flour and 1000 grams of butter, which is more than enough to make 12 cupcakes. However, the recipe requires 3/4 cup of sugar, 2 eggs, and 3/4 cup of milk, which we do not know if Duri has enough of.
Habib has 3 cups of milk and 6 cups of sugar, which is enough to make 12 cupcakes.
Anika has 1 cup of sugar and 4 cups of milk, which is not enough to make 12 cupcakes.
Therefore, only Duri and Habib have enough ingredients to make 12 cupcakes on their own.
To determine how many cupcakes they can make, we need to calculate how much of each ingredient is required for one cupcake and then divide the available ingredients by that amount.
For one cupcake, we need:
1/6 cups of flour
1/16 cup of sugar
1/6 eggs
1/16 cups of milk
125/12 grams of butter
Duri has 12 cups of flour and 1000 grams of butter, which is enough to make 72 cupcakes. Habib has 6 cups of sugar and 3 cups of milk, which is enough to make 36 cupcakes.
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what is the volume, in cubic centimeters, of a right rectangular prism that has a length of 4 44 centimeters, a width of 9 99 centimeters, and a height of 10 1010 centimeters?
Step-by-step explanation:
Volume of rect prism = L X W X H = 4 X 9 X 10 = 360 cm^3
one more than the reciprocal of a particular number is $\frac{7}{3}$. what is the original number expressed as a common fraction?
Original number = $\frac{3}{4}$. The original number expressed as a common fraction is $\frac{3}{4}$.
1. Reciprocal: This is the result of switching the numerator and denominator of a fraction (or dividing 1 by a whole number).
2. Original number: This is the number we're trying to find.
3. Common fraction: This is a fraction where the numerator and denominator are both integers (whole numbers).
Step 1: Set up the equation using the given information.
One more than the reciprocal of the original number is $\frac{7}{3}$. We can express this as an equation:
Reciprocal of the original number + 1 = $\frac{7}{3}$
Step 2: Solve for the reciprocal of the original number.
Reciprocal of the original number = $\frac{7}{3}$ - 1
Step 3: Simplify the equation.
Reciprocal of the original number = $\frac{7}{3}$ - $\frac{3}{3}$
Reciprocal of the original number = $\frac{4}{3}$
Step 4: Find the original number.
Since we have the reciprocal of the original number, we can find the original number by taking the reciprocal of this value:
Original number = $\frac{1}{(\frac{4}{3})}$
Step 5: Simplify the expression.
Original number = $\frac{1}{1} \times \frac{3}{4}$
Original number = $\frac{3}{4}$
The original number expressed as a common fraction is $\frac{3}{4}$.
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Could anyone help? I genuinely don't understand what the question is asking. All I need. is for you to set up the equations for me. An answer isn't necessary unless you'd like to be marked brainliest.
Answer:
9) Keep the denominators the same, and subtract the numerators. Then simplify if necessary.
[tex] \frac{3x + 2}{x + 5} - \frac{2x - 3}{x + 5} [/tex]
[tex] = \frac{3x + 2 - (2x - 3)}{x + 5} [/tex]
[tex] = \frac{3x + 2 - 2x + 3}{x + 5} [/tex]
[tex] \frac{x + 5}{x + 5} = 1[/tex]
10) Find the LCD. Rewrite each rational expression as an equivalent expression with the LCD as the denominator. Add the numerators and write the sum over the LCD. Then simplify if necessary.
[tex] \frac{4x}{x - 2} + \frac{x - 4}{x - 5} [/tex]
[tex] = \frac{4x(x - 5) + (x - 4)(x - 2)}{(x - 2)(x - 5)} [/tex]
[tex] = \frac{4 {x}^{2} - 20x + {x}^{2} - 6x + 8 }{(x - 2)(x - 5)} [/tex]
[tex] = \frac{5 {x}^{2} - 26x + 8}{(x - 2)(x - 5)} [/tex]
[tex] = \frac{5 {x}^{2} - 26x + 8 }{ {x}^{2} - 7x + 10} [/tex]
The recipe for one batch of
chocolate chip cookies calls
for 11/3 cups of chocolate
chips. Luca made 3½ batches
of cookies. How many cups of
chocolate chips did he use?
Answer:
Step-by-step explanation:
1 + 1 divided by 3 x 3.5 = 4.66 or 4 2/3
what is the probability that a simple random sample of 50 ten-gram portions results in a mean of at least 3.6 insect fragments? is this result unusual? what might we conclude?
a) The probability that a simple random sample of 50 ten-gram portions results in a mean of at least 3.6 insect fragments is approximately 0.027.
b) This result is somewhat unusual, as only about 2.7% of samples would be expected to have a mean of at least 3.6 insect fragments. However, it is not necessarily a cause for concern, as it is within the range of expected variation.
c) More information about the distribution of insect fragments in the population and the context in which the samples were collected would be needed to draw more definitive conclusions.
To answer this question, we would need to know the distribution of insect fragments in the population from which the samples are drawn. Let's assume that this distribution is approximately normal with a mean of 3.2 insect fragments and a standard deviation of 0.8 insect fragments, as suggested by FDA guidelines for chocolate.
The distribution of the sample means for samples of size n can be approximated by a normal distribution with mean µ and standard deviation σ/√n. In this case, µ = 3.2 and σ/√n = 0.8/√50 = 0.113.
To find the probability that a sample of 50 ten-gram portions has a mean of at least 3.6 insect fragments, we need to find the area under the normal curve to the right of 3.6. Using a standard normal distribution table or a calculator, we find that this probability is approximately 0.027.
This result is somewhat unusual, as only about 2.7% of samples would be expected to have a mean of at least 3.6 insect fragments. However, it is not necessarily a cause for concern, as it is within the range of expected variation. If the sample mean was much higher, say 4.0 or 4.5, it would be more concerning and warrant further investigation.
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6. Electronics Warehouse had a Super Bowl Sale on Televisions. They offered no interest no payments for 24 months on televisions larger than 50 inches. You have been dving to have a new 85" TV, so you pick out an amazing OLED on sale for $2299.99. You take advantage of the store offering no interest, no paymenus for 24 months, and go home smiling. The fine print on the credit card agreement states a 24.99% interest rate that accrues monthly. Additionallv. if the balance is not paid in full by the end of the 24 month promotion. the interest will be apolied to the remaining balance. If vou choose to not make a payment during the 24-month period, what will your balance be when you get your first bill?
If you choose not to make a payment during the 24-month period, your balance at the end of the promotion will be $3,637.16.
Explain month
A month is a unit of time equal to one-twelfth of a year, or approximately 30.44 days. It is often used to represent periodic phenomena, such as interest rates or seasonal trends, and to calculate the duration between two dates. The number of months between two dates is calculated by dividing the difference in days by 30.44.
According to the given information
If you do not make any payments during the 24-month period, your balance will increase each month due to the interest that accrues. After 24 months, your balance will be:
$2299.99 * (1 + 0.020825)²⁴ = $3,637.16
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what is the summation notation for 8+4+2+1+1/2
Answer:
15 1/2
Step-by-step explanation:
hope this helped
if 15% of adults in a certain country work from home, what is the probability that fewer than 30 out of a random sample of 250 adults will work from home?
The probability regarding fewer than 30 people out of 250 people will consider working from home is 3.36%.
In order to calculate the probability for the given condition we need to perform binomial distribution
P(X < 30) = Σ P(X = x)
For x = 0 to 29
Here,
X = number of people from the sample who work from home
P = probability of an adult working from home
Given,
X = 250
P = 0.15
Now performing approximation to binomial distribution, leads to approximate X like a normal random variable with mean
Therefore,
μ = np
μ = 250 x 0.15
μ = 37.5
Now we have to evaluate the standard deviation
σ = √(np(1-p))
σ = √ 250 x 0.15 x (1 - 0.15)
σ ≈ 4.08
Then we can proceed to standardized X
Z = (X - μ) / σ
P(X < 30) = P(Z < (30 - μ) / σ) = P(Z < (30 - 37.5) / 4.08)
≈ P(Z < -1.84)
Using standard distribution table
P(Z < -1.84) ≈ 0.0336
Converting it into percentage
0.0336 x 100
= 3.36%
The probability regarding fewer than 30 people out of 250 people will consider working from home is 3.36%.
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PLEASE HELP ILL MARK U AS BRAINLIEST!!
Answer: 64 sqaure centimetres.
Step-by-step explanation:
- Surface area means the area of all exterior sides of a 3D dimensional shape. This means we'll have to find the area of every face and then add them all together.
Top and Bottom
4 x 4 = 16
16 x 2 = 32
Both faces are the same so once we find the area of one, we can just double it.
North, South, East and West Side
4 x 2 = 8
8 x 4 = 32
All four remaining faces had the same dimensions, meaning that once you found one, you just had to multiply that answer by 4.
To find the overall surface area add all the areas you have.
32 + 32 = 64
or
16 +_16 + 8 + 8 + 8 + 8 = 64
In ΔHIJ, the measure of ∠J=90°, HI = 6. 7 feet, and JH = 4. 8 feet. Find the measure of ∠I to the nearest degree
The measure of angle I in the triangle HIJ using given measurements is equal to 46.05 degrees.
In the triangle HIJ,
The measure of angle J is equal to 90 degrees.
This implies ,
HI is the hypotenuse.
JH is the opposite side to angle I.
In triangle HIJ,
Using trigonometric ratio we get,
sin ∠I = Opposite side / Hypotenuse
Substitute the values we have,
⇒ sin ∠I = 4.8 / 6.7
⇒ sin ∠I = 0.72
Now , take sin⁻¹ both the side of the equation we get,
⇒sin⁻¹(sin ∠I) = sin⁻¹( 0.72 )
Here sin⁻¹(sin ∠I) = ∠I
⇒∠I = sin⁻¹( 0.72 )
⇒∠I = 46.05 degrees
Therefore, the measure of angle I is equal to 46.05 degrees.
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In artwork consists of the triangle shown with the shaded triangle is cut out of the larger triangle. What is the area of the remaining unshaded portion?
Thus, the area of unshaded portion for the given values of triangle is found as 48.6 sq. m.
Explain about the triangle:Three sides, three angles, plus three vertices make up a triangle.
A triangle's total internal angles have always been equal to 180 degrees. This is referred to as the triangle's angle sum property.The greatest side of a triangle is the side that faces the largest angle.The sum of the triangle's internal opposite angles is equal to any of its outer angles. This is referred to as the triangle's outside angle property.Area of triangle = 1/2*base *height
Area of unshaded portion = complete area - area of shaded triangle
Area of unshaded portion = 1/2*(20)*(8.1) - 1/2*8*(8.1)
Area of unshaded portion = 81 - 32.4
Area of unshaded portion = 48.6
Thus, the area of unshaded portion for the given values of triangle is found as 48.6 sq. m.
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a region is bounded by two concentric circles, as shown by the shaded region in the figure above. the radius of the outer circle, r , is increasing at a constant rate of 2 inches per second. the radius of the inner circle, r , is decreasing at a constant rate of 1 inch per second. what is the rate of change, in square inches per second, of the area of the region at the instant when r is 4 inches and r is 3 inches? responses
The rate of change of the area is 20π square inches per second.
How to calculate area of the shaded region?The area of the shaded region can be calculated as the difference between the areas of the outer circle and the inner circle:
A = πr^2 - πr'^2
where r is the radius of the outer circle, r' is the radius of the inner circle, and π is the constant pi.
To find the rate of change of the area, we can take the derivative of both sides of the equation with respect to time t:
dA/dt = d/dt (πr^2) - d/dt (πr'^2)
Using the chain rule, we can express the derivatives in terms of the rates of change of the radii:
dA/dt = 2πr (dr/dt) - 2πr' (dr'/dt)
Substituting the given values at the instant when r=4 inches and r'=3 inches, we have:
dA/dt = 2π(4)(2) - 2π(3)(-1) = 20π
Therefore, the rate of change of the area is 20π square inches per second.
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Helpp (30,60,90) and (45,45,90) but in radical form
Answer:
In its simplest form, the ratios of the length of sides in a 45 45 90 special right angle triangles should be 1 : 1 : 2 1:1:\sqrt{2} 1:1:2on:
And because this is a 30-60-90 triangle, and we were told that the shortest side is 8, the hypotenuse must be 16 and the missing side must be 8 * 3 , or 8 3 . Our final answer is 8√3
A dog named Bella has a rectangular bed that is 2 feet wide and 3 feet long. A larger dog, Kahuna, has a rectangular bed which is 5x feet wider and 8x feet longer than Bella's bed.
Which of the following equations could be used to determine the area of Kahuna's bed?
The equation that could be used to determine the area of Kahuna's bed is:
Area = 12 + 32xHow to find the equation for the areaThe area of Kahuna's bed can be determined by multiplying its length by its width.
Let's first determine the length and width of Kahuna's bed in terms of x.
The width of Kahuna's bed is 2 feet wider than Bella's bed, which means its width is:
2 + 2 = 4 feet
The length of Kahuna's bed is 8x feet longer than Bella's bed, which means its length is:
3 + 8x
Therefore, the area of Kahuna's bed can be calculated as:
Area = length x width
Area = (3 + 8x) x 4
Expanding the equation, we get:
Area = 12 + 32x
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2. Which sequence of transformations takes the graph of y = k(x) to the graph of
y=-k(x + 1)?
A. Translate 1 to the right, reflect over the x-axis, then scale vertically by a factor of 1/2
B. Translate 1 to the left, scale vertically by 1/2 , then reflect over the y-axis.
C. Translate left by 1/2, then translate up 1.
D. Scale vertically by 1/2, reflect over the x-axis, then translate up 1.
The correct answer is option B. Translate 1 to the left, scale vertically by 1/2, then reflect over the y-axis.
What does term "transformation of a graph" means?The process of modifying the shape, location, or features of a graph is often referred to as graph transformation. Graphs are visual representations of mathematical functions or data point connections, often represented on a coordinate plane.
Translations, reflections, rotations, dilations, and other changes to the look of a graph are examples of graph transformations.
For the given problem, Transformation to get the desired result can be carried out as:
Translate '1' to the left: The transformation "x + 1" in "-k(x + 1)" shifts the graph horizontally to the left by 1 unit.Scale vertically by '1/2' : The 1/2 factor in "-k(x + 1)" vertically scales the graph, compressing it vertically.Reflect over the y-axis: The minus sign before "k" in "-k(x + 1)" reflects the graph over the y-axis, flipping it horizontally.Hence, to convert the graph of "y = k(x)" to the graph of "y = -k(x + 1)," the correct sequence of transformations is to translate 1 unit to the left, scale vertically by 1/2, and then reflect across the y-axis, which is option B.
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WILL MARK BRAINLIST PLS HELP!!
(-4,-5); slope = 1/2
Answer: y=1/2x-3
Step-by-step explanation:
I'm assuming you're trying to find it in slope intercept form!
y=mx+b
y=1/2x-3
easy
In a class of students, the following data table summarizes how many students passed a test and complete the homework due the day of the test. What is the probability that a student who did not complete the homework passed the test?
The probability that a student who did not complete the homework passed the test is 0.25.
cara computes the mean and variance for the set 87, 46, 90, 78, and 89. she finds the mean to be 78. her steps for finding the variance are shown below. what is the first error cara made in computing the variance?
If Cara's calculation of the sum of the squared differences i.e. 1370 from the mean is incorrect, that would be the first error she made in computing the variance.
As the steps for finding the variance are not provided, it is difficult to determine the first error Cara made.
However, the formula for calculating the variance is:
Variance = (sum of the squared differences from the mean) / (number of observations)
The first error Cara may have made is in calculating the sum of the squared differences from the mean.
The correct steps to find the variance are:
Find the mean:
Mean = (87 + 46 + 90 + 78 + 89) / 5 = 78
Calculate the differences from the mean for each observation:
87 - 78 = 9
46 - 78 = -32
90 - 78 = 12
78 - 78 = 0
89 - 78 = 11
Square each difference:
[tex]9^2 = 81[/tex]
[tex](-32)^2 = 1024[/tex]
[tex]12^2 = 144[/tex]
[tex]0^2 = 0[/tex]
[tex]11^2 = 121[/tex]
Find the sum of the squared differences:
81 + 1024 + 144 + 0 + 121 = 1370
Divide the sum of squared differences by the number of observations:
Variance = 1370 / 5 = 274.
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True or False. (a). X(x^2 + 4)/x^2 - 4 can be written as (A/x + 2)+ (B/x - 2)
(b). X^2 + 4/x(x^2 - 4) can be written as (A/x) + (B / x + 2) + (C/x - 2). (c). X^2 + 4/x^2(x - 4) can be written as (A/x^2) + (B/x - 4)
(d). X^2 - 4/x(x^2 + 4) can be written as (A/x) + (B / x^2 + 4)
(a) True. We can use partial fraction decomposition to write X(x² + 4)/(x² - 4) as (A/(x+2)) + (B/(x-2)).
(b) True. We can use partial fraction decomposition to write X² + 4/(x(x² - 4)) as (A/x) + (B/(x+2)) + (C/(x-2)).
(c) True. We can use partial fraction decomposition to write X² + 4/(x²(x - 4)) as (A/x²) + (B/x) + (C/(x-4)).
(d) False. We can use partial fraction decomposition to write X² - 4/(x(x² + 4)) as (A/x) + (Bx+C)/(x²+4).
(a) We want to write X(x² + 4)/(x² - 4) in the form (A/(x+2)) + (B/(x-2)). First, we find A and B by multiplying both sides by the common denominator (x+2)(x-2):
X(x² + 4) = A(x-2) + B(x+2)
Expanding both sides gives:
Xx² + 4X = Ax - 2A + Bx + 2B
Grouping terms by x gives:
Xx² + (A+B)x + (-2A+2B) = 4X
Now we have a system of two equations:
A + B = 0 (coefficients of x)
-2A + 2B = 4X (constant terms)
Solving for A and B gives:
A = -B
-2A + 2B = 4X
-2A + 2(-A) = 4X
-4A = 4X
A = -X
Therefore, B = X. Thus,
X(x² + 4)/(x² - 4) = (-X/(x+2)) + (X/(x-2))
(b) We want to write X² + 4/(x(x² - 4)) in the form (A/x) + (B/(x+2)) + (C/(x-2)). First, we find A, B, and C by multiplying both sides by the common denominator x(x+2)(x-2):
X² + 4 = A(x+2)(x-2) + Bx(x-2) + Cx(x+2)
Expanding both sides gives:
X² + 4 = Ax² - 4A + Bx² - 2Bx + Cx^2 + 2Cx
Grouping terms by powers of x gives:
(X² + 4) = (A+B+C)x² + (-2B+2C)x - 4A
Now we have a system of three equations:
A + B + C = 0 (coefficients of x²)
-2B + 2C = 0 (coefficients of x)
-4A = 4 (constant terms)
Solving for A, B, and C gives:
A = -1/4
B = 1/4
C = 1/4
Therefore,
X² + 4/(x(x² - 4)) = (-1/(4x)) + (1/(4(x+2))) + (1/(4(x-2)))
(c) We want to write X² + 4/(x²(x - 4)) in the form (A/x²) + (B/x) + (C/(x-4)). First, we find A, B, and C by multiplying both sides by the common denominator x²(x-4):
X²(x-4) + 4x² = Ax(x-4) + Bx²(x-4) + Cx²
Expanding both sides gives:
X²x - 4X² + 4x² = Ax² - 4Ax + Bx³ - 4Bx² + Cx²
Grouping terms by powers of x gives:
(X² + 4) = (B)x³ + (A-4B)x² + (-4A+C)x
Now that we have a common denominator of (x² - 4), we can combine the two fractions and simplify:
X(x² + 4) - 2(x² - 4) = A(x - 2) + B(x + 2)
Expanding and simplifying the left side:
x³ + 4x - 2x² + 8 = Ax - 2A + Bx + 2B
Grouping the like terms on each side:
x³ - 2x² + Ax + Bx + 4x - 2A + 2B + 8 = 0
Now we have a polynomial equation that we can use to solve for A and B. We can do this by equating the coefficients of like terms on both sides. Specifically, we can equate the coefficients of x² and x:
x³ - 2x² + Ax + Bx + 4x - 2A + 2B + 8 = 0
Coefficients of x²: -2 = A
Coefficients of x: 4 = B
Therefore, we have:
X(x² + 4)/(x² - 4) = (-2x)/(x² - 4) + (4)/(x² - 4)
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tim wants his mean quiz score to be 90. his first 3 quiz scores were 86, 92, and 94. what score should he make on the 4th quiz in order to have a mean quiz score of exactly 90?
The score to be made on the 4th quiz in order to have a mean quiz score of exactly 90 is equal to 88.
Let us consider the score that Tim needs to get on his fourth quiz be x.
Score he needs to get in order to have a mean quiz score of 90,
Set up an equation using the formula for the mean ,
(mean score) = (sum of scores) / (number of scores)
If Tim wants his mean quiz score to be 90, then we have,
⇒ 90 = (86 + 92 + 94 + x) / 4
Multiplying both sides by 4, we get,
⇒360 = 86 + 92 + 94 + x
Simplifying this equation, we get,
⇒ x = 360 - 272
⇒ x = 88
Therefore, Tim needs to get a score of 88 on his fourth quiz in order to have a mean quiz score of exactly 90.
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Find the exact value of cos a, given a=-3/7 and a is in quadrant 4
Answer:
9.955
Step-by-step explanation: