Therefore , the solution of the given problem of rectangle comes out to be A= b* √6²-b².
Describe the rectangle.In the Euclidean plane, a rectangle is merely a cube with four right angles. It is sometimes referred to as an equiangular quadrilateral or a quadrant that seems to have equal angles. The parallelogram also has the option of a straight angle. Four of a square's sides are all the same length. Rectangular quadrilaterals have four equal sides and four 90° vertices. It is sometimes referred as an "equirectangular square" as a result. A rectangle is also referred to as a parallelogram due to the identical and parallel lengths of its opposite sides.
Here,
radio= 3 cm
Al estar un rectángulo inscrito en un círculo, el diámetro del círculo corresponderá a la diagonal del rectángulo
Siendo b la base del rectángulo y a la altura, se tiene que:
6²= a²+b²
a²= √6²-b²
Nota: Se empleó el teorema de Pitágoras
El área del rectángulo está dado por:
A= base* altura
A= b*a
Reemplazando a:
A= b* √6²-b²
Therefore , the solution of the given problem of rectangle comes out to be A= b* √6²-b².
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sketch the region enclosed by the given curves. decide whether to integrate with respect to x or y. draw a typical approximating rectangle. 2x y2
The area between the curves is 18 square units.
First, we should find the area between the curves 2x+y²=8 and y=x, we can find the area of curves by substituting y for x in equation 2x+y²=8.
The given equation is 2x+y²=8 and for this, we have to find the roots:
2y+y²=8
y²+2y−8=0
(y+4)(y−2)=8
so the line y=x intersects the parabola 2x+y²=8 at the points (−4,−4) and (2,2). Solving the equation 2x+y²=8 for x yields x=4−1/2y²
From sketching the graphs of the parabola and the line, we can see that the x-values on the parabola lie on the line in the interval of −4≤y≤2.
The area between curves is:
[tex]A=\int\limits^2_4 {(4-\frac{1}{2}y^2-y) } \, dy\\\\A=(4y-\frac{1}{6} y^3-\frac{1}{2} )^2_-_4[/tex]
A=(8-4/3-2)-(-16+32/3-8)
A =18 square units.
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.
. State whether the image below is an enlargement
or a reduction. Identify the scale factor.
4cm
15
3cm
5cm
20cm
25cm
15cm
Enlargement OR Reduction? (circle one)
Scale Factor =
The image below is a reduction, the scale factor is 1/5.
How to calculate the scale factor?Suppose the initial measurement of a figure was x units.
And let the figure is scaled and new measurement is of y units.
Since the scaling is done by multiplication of some constant, that constant is called scale factor. Let that constant be 's'.
Then we have:
[tex]s \times x = y\\s = \dfrac{y}{x}[/tex]
Thus, scale factor is the ratio of the new measurement to the old measurement.
Given;
The two triangle with 4cm, 5cm, 3cm and 20cm, 25cm, and 15cm.
Now,
s=4/20=1/5
s=5/25=1/5
s=3/15=1/5
Therefore, the scale factor will be 1/5.
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ii. The first four moments of a distribution about the value 4 of the variable are -1.5, 17,-30 and 108. Find the moments about mean.
Answer:2.5,21,166,1132
Step-by-step explanation:
Hi can someone please help me with these questions I'm really struggling with them!!!
(Is anyone really good at math? )
Image 1
1.
2.
3.
Image 2
1.
2.
3.
Answer:
image 2
1. SSS
2. AAS
3. SAS
Which line best models line l?
The linear function that best models line l is given as follows:
F. x = 4.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
For which the parameters are given as follows:
m is the slope, representing the rate of change.b is the intercept, representing the value of y when x = 0.For a vertical line, the slope is undefined, hence the function is given as follows:
x = c.
The function in this problem has a x-coordinate of 4 for all values of y, hence it is defined as follows:
x = 4.
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Which equation represents the written description?
Five times the difference between 26.8 and a number is equal to 63.7.
5(m − 26.8) = 63.7
5m − 26.8 = 63.7
5(26.8 − m) = 63.7
5(26.8) − m = 63.7
Answer:
The first one is the answer
Step-by-step explanation:
let m be the other number,
so 5(m-26.8) = 63.7
the small round holes you often see in sea shells were drilled by other sea creatures, who ate the former dwellers of the shells. whelks often drill into mussels, but this behavior appears to be more or less common in different locations. researchers collected whelk eggs from the coast of oregon, raised the whelks in the laboratory, then put each whelk in a container with some delicious mussels. only 9 of 98 whelks drilled into a mussel.11 the researchers want to estimate the proportion p of oregon whelks that will spontaneously drill into mussels.
We estimate that, based on the sample, 9.18% of Oregon whelks will drill into mussels.
We can calculate the estimated proportion of Oregon whelks that will drill into mussels by using the following formula: [tex]$\hat{p} = \frac{x}{n}$[/tex], where x is the number of whelks that drilled into mussels and $n$ is the total number of whelks in the sample.
In this example, x is equal to 9, and n is equal to 98. Thus, the estimated proportion of Oregon whelks that will drill into mussels is [tex]$\hat{p} = \frac{9}{98} = 0.0918$[/tex]. This means that, based on the sample, we estimate that 9.18% of Oregon whelks will drill into mussels.
We estimate that, based on the sample, 9.18% of Oregon whelks will drill into mussels.
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Order the steps for solving the equation:
2x - 5 = 3(4x + 5)
Bank:
- Distributive Property; 2x - 5 = 12x + 15
- Subtract 15; -20 = 10x
- Subtract 2x; -5 = 10x + 15
- Divide by 10; -2 = x
Ten people ordered calculators. The least expensive was $29.95 in the most expensive is $69.95 half of them ordered and $39.95 calculator select the best estimate of the amount spent on calculators.
A mean is an arithmetic average of a set of observations. The correct option is D.
What is Mean and how to calculate the mean?A mean is an arithmetic average of a set of observations. It is given by the formula,
Mean = (Sum of observations)/Number of observations
To make the calculations easy let's round off the given numbers. Therefore, we can write the values as,
Least expensive A=30
Most expensive B=90
half of order C=70
Now, the mean and the money for half the people can be written as,
Mean = (least + most)/2 = 60
money for half people = 5 × 60
Therefore, the amount of money for half people will be,
Amount of money for half people = 300
Lower limit for amount of the other half = 29.95 × 5 = 149.5
The Upper limit for the amount of the other half = 89.95 × 5 = 449.75
Mean = (149.75 + 449.75)/2 = 299.6Total money spent (Mean) = 299.6 + 299.6 = 599.25
Hence, The Best estimate is $660. This is because it is closest to 599.25.
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Ten people ordered calculators. The least expensive was $19.95 and the most expensive was$39.95. Half ordered a $29.95 calculator. Select the best estimate of the amount spent on calculators.
a.$240,
b. $310,
c.$345,
d. $355
rearrange w=3(2a+b)-4
make a the subject
Step-by-step explanation:
Rearrange w = 3(2a + b) - 4 to make a the subject:
w = 3(2a + b) - 4
expand right side:
w = 6a + 3b - 4
add 4 to both sides:
w + 4 = 6a + 3b - 4 + 4
w + 4 = 6a + 3b
subtract 3b from both sides:
w + 4 - 3b = 6a + 3b - 3b
w + 4 - 3b = 6a
flip flop equation for readability ease:
w + 4 - 3b = 6a becomes:
6a = w + 4 - 3b
divide both sides by 6:
6a/6 = (w + 4 - 3b)/6
a = [tex]\frac{1}{6}w + \frac{4}{6} -\frac{3}{6}b[/tex]
reduce:
a = [tex]\frac{1}{6}w + \frac{2}{3} -\frac{1}{2}b[/tex]
Now, arrange right side of equation so variables are ordered alphabetically.
Answer: [tex]a = -\frac{1}{2}b +\frac{1}{6} w+\frac{2}{3}[/tex]
Which of the following is an even function?
The solution is, f(x) = 7 is a even function.
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have,
Solution:
Given that we have to find the even function
A function is even if and only if f(–x) = f(x)
Steps to follow:
Replace x with -x and compare the result to f(x).
If f(-x) = f(x), the function is even.
If f(-x) = - f(x), the function is odd.
If f(-x) ≠ f(x) and f(-x) ≠ -f(x), the function is neither even nor odd.
now,
Option 4
f(x) = 7
f(-x) = 7
Thus f(-x) = f(x)
Thus it is a even function.
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The school cafeteria is selling hot dogs for $2 and chili dogs for $2.50. They sold 53 items for a total of $120. How many hot dogs were sold. How many chili dogs were sold
Answer:
Hotdogs = 25 Chili dogs = 28
I believe it correct
advertising is an example of a activity. activity-based costing accumulates costs for each .
Activity-based costing is a method of assigning overhead costs to activities and then assigning those costs to products, and is calculated by dividing total overhead cost by total number of activities and multiplying by the number of activity units associated with the activity.
Activity-based costing (ABC) is a costing method that assigns costs to activities within an organization, and then assigns the cost of those activities to products. The goal of ABC is to more accurately assign overhead costs to products or services. ABC begins by assigning a cost to each activity based on the cost of the resources used to complete the activity. This is normally done by gathering cost data from different departments and then assigning overhead costs to each activity.
For example, the formula for activity-based costing is:
Activity Cost = (Total Overhead Cost / Total Number of Activities) x Number of Activity Units
For example, if a company has total overhead costs of $100,000 and 10 different activities, the cost for each activity would be $10,000. If one of those activities had 10 units associated with it, the cost of that activity would be $1,000 (or $10,000/10 x 10).
Once the cost of each activity is determined, the cost of the activity can be assigned to the products or services that use the activity. This allows the company to better understand the cost associated with each product or service. By understanding the costs associated with each product and service, the company can better manage the costs associated with producing and selling their products.
Activity-based costing is a method of assigning overhead costs to activities and then assigning those costs to products, and is calculated by dividing total overhead cost by total number of activities and multiplying by the number of activity units associated with the activity.
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One leg of a right triangle has a length of 7m. The other sides have lengths that are consecutive integers. Find the lengths
Answer:
24 m, 25 m
Step-by-step explanation:
You want the two sides of a right triangle that are consecutive integers when one side is 7 m.
Pythagorean theoremLet the shorter side be represented by x. Then the longer side is x+1, and the Pythagorean theorem tells you ...
7² +x² = (x+1)²
49 +x² = x² +2x +1
48 = 2x . . . . . . subtract (x²+1)
24 = x
x+1 = 25
The other sides are 24 and 25 meters.
__
Additional comment
You know that 7 is not the hypotenuse, because a 3-4-5 right triangle is the only right triangle with consecutive integer leg lengths and a hypotenuse of 7 or less. (The next nearest right triangle with consecutive leg lengths is {20, 21, 29}, with a hypotenuse of 29.)
You may recognize the side lengths as the Pythagorean Triple {7, 24, 25}, one of the triples commonly seen in algebra and trig problems.
Sharonda uses a blend of dark chocolate and milk chocolate to make the ice cream topping at her restaurant. She needs to buy 120\,\text{kg}120kg120, start text, k, g, end text of chocolate in total for her next order, and her recipe calls for twice the amount of dark chocolate as milk chocolate.
Let ddd be the number of kilograms of dark chocolate she buys and mmm be the number of kilograms of milk chocolate she buys.
Which system of equations represents this situation?
The system of equations that represent this situation is given as follows:
d + m = 120.7d = 2m.How to model the system of equations?The variables for the system of equations are given as follows:
Variable d: number of kilograms of dark chocolate.Variable m: number of kilograms of milk chocolate.The total weight is of 120 kg, hence the first equation is given as follows:
d + m = 120.
Her recipe calls for twice the amount of dark chocolate as milk chocolate, hence the second equation is given as follows:
d = 2m.
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What kind of angle is this
Answer:
no they are not similar
Step-by-step explanation:
Answer:
SAS
Step-by-step explanation: :)
Write the general antiderivative of the given rate of change function. (Use C for the constant of integration.) The rate of change of DVD orders is given by where m is the number of months since the beginning of the year. s(m) - 500m +8 DVDs per month S(m) DVDs
The total number of DVDs ordered after m months since the beginning of the year.
The antiderivative of the rate of change of DVD orders can be represented by the general equation: S(m) = 500m^2/2 + 8m + C. To calculate the antiderivative, we first need to find the integral of the function. We can do this by multiplying the rate of change by the differential of m, which is just dm. This gives us 500m^2/2 + 8m, which is our integrand. Finally, we integrate this expression with respect to m to get our desired antiderivative. This gives us 500m^2/2 + 8m + C, where C is the constant of integration. This equation represents the total number of DVDs ordered after m months since the beginning of the year.
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FIND THE VOLUME OF THE PRISM 10b 3w 4h
Answer:
120
Step-by-step explanation:
To find the volume you multiply L = 10, W = 3, and H = 4
10 x 3 x 4
30 x 4
120
Question 1
Use dimensional analysis to convert.
How many ounces (oz) are in 46 quarts (qt)? (1 qt = 4 cups, 1 cup = 8 oz)
To convert 46 qt to ounces, you must first convert 46 qt to cups.
Which expression correctly shows the measurement multiplied by the conversion factor?
Responses
46 qt1⋅1 qt4 cups46 qt 1 · 1 qt 4 cups
46 qt1⋅4 cups1 qt46 qt 1 · 4 cups 1 qt
146 qt⋅1 qt4 cups1 46 qt · 1 qt 4 cups
146 qt⋅1 cup1 qt1 46 qt · 1 cup 1 qt
The solution is, 46 quarts (qt) = 46*4*8 oz
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
1 qt = 4 cups,
1 cup = 8 oz
so, we get,
46 quarts (qt) = 46*4 cup
i.e. 46 quarts (qt) = 46*4*8 oz
Hence, The solution is, 46 quarts (qt) = 46*4*8 oz
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The width of a rectangle is 7y-9.5 feet and the length is 9.5y + 10 feet. Find the perimeter of the rectangle
Answer:
So the perimeter of the rectangle is 33y + 1 feet.
Step-by-step explanation:
Let's call the width of the rectangle "w" and the length "l". From the given information, we have:
w = 7y - 9.5
l = 9.5y + 10
The perimeter of a rectangle is equal to the sum of the lengths of all four sides, so we can find the perimeter by adding up the values of w and l:
P = 2w + 2l
= 2(7y - 9.5) + 2(9.5y + 10)
= 14y - 19 + 19y + 20
= 33y + 1
So the perimeter of the rectangle is 33y + 1 feet.
Answer:
Rectangle
Solve for perimeter
P=33
length =9.5
Width =7
Step-by-step explanation:
the answer is 33
Hope this helps!!
The dog shelter has Labradors, Terriers, and Golden Retrievers available for adoption. If P(terriers) = 15%, interpret the likelihood of randomly selecting a terrier from the shelter.
Likely
Unlikely
Equally likely and unlikely
This value is not possible to represent probability of a chance event
Answer:
Likely.
Step-by-step explanation:
so easy that is
or you need explanation?
Morgan has two sisters. Morgan is x years old. Her sister Megan is 3 years older. Her sister Marie is 2 years older. Which expression represents the sum ○ A. x+5 ○ B. x+8 o C. 3x+5 o D. 3x+8
Answer:
C
Step-by-step explanation:
morgan = x
megan = x+3
marie = x+2
x+x+3+x+2=3x+5
PLEASE HELP 20 points
Answer: Im pretty sure the answers are B and C
Step-by-step explanation:
if you start with [tex]\frac{2(3x-6)}{3}[/tex] and distribute the 2
[tex]2*3=6[/tex]
[tex]2*-6=-12[/tex]
So you are left with [tex]\frac{6x-12}{3}[/tex]
[tex]\frac{6x}{3}=2x[/tex]
[tex]\frac{-12}{3}=-4[/tex]
[tex]2x-4[/tex]
nUmeRIC
For the following exercises, perform the indicated operation and express the result as a simplified complex number.
(3 + 2i) + (5 − 3i)
. (−5 + 3i) − (6 − I)
(−4 + 4i) − (−6 + 9i)
(2 + 3i)(4 − i)
2-3i/4+3i
The simplified form of complex number (2+3i)(4-i) is 11+10i.
What is the complex number?A complex number is the sum of a real number and an imaginary number. A complex number is of the form a + ib and is usually represented by z.
Here,
A) (3 + 2i) + (5 - 3i)
= 3+2i+5-3i
= 8-i
B) (-5 + 3i) - (6 - i)
= -5+3i-6+i
= -11+4i
C) (-4+4i)-(-6+9i)
= -4+4i+6-9i
= 2-5i
D) (2+3i)(4-i)
= 8+12i-2i-3i²
= 8+10i+3
= 11+10i
E) (2-3i)/(4+3i)
Rationalize denominator, that is
(2-3i)×(4-3i)/(4+3i)×(4-3i)
= (8-12i-6i+9i²)/(16-9i²)
= (8-18i-9)/25
= (-18i-1)/25
Therefore, the simplified form of (2+3i)(4-i) is 11+10i.
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Central Middle School has a triangular patio where students eat lunch. A scale drawing of the patio is shown. The scale is 1 in. : 9 ft. What is the area of the patio in the drawing? When the base and height are: 5 and 4? What is the area in the drawing?
The area of triangular patio = 810 sq. ft
and In drawing, The area of triangle = 10 sq. In
What is area of triangle?A triangle is a closed figure that has three vertices, three sides, and three angles. The entire area filled by a triangle's three sides in a two-dimensional plane is referred to as the triangle's area. The fundamental equation for a triangle's area is A = 1/2 b h, where b and h are the product of the triangle's base and height.
Given that in drawing the base and height of a triangular patio are: 5 In and 4 In.
and A scale drawing of the patio is 1 in. : 9 ft
So that the the base and height of a triangular patio are 5*9 ft = 45ft and 4*9 ft = 36 ft
The area of triangular patio = 1/2 * base * height
The area of triangular patio = 1/2 * 45 * 36 sq. ft
The area of triangular patio = 810 sq. ft
In drawing, The area of triangle = 1/2 * base * height
The area of triangle = 1/2 * 5 * 4 sq. In
The area of triangle = 10 sq. In
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a random number is selected uniformly from 0; 1; 2; 3; 4; 5; 6; 7 without replacement until 3 is chosen. let x denote the number of selection. find the entropy h(x) in bits
The entropy of the random variable X in this case is approximately 1.585 bits.
The entropy of a random variable X is a measure of the uncertainty associated with it. In this case, the random variable X is the number of selections required to choose the number 3.
Since the numbers are selected without replacement, the possible values for X are 1, 2, and 3, and the probabilities for each value are:
P(X=1) = 1/3
P(X=2) = 2/7
P(X=3) = 4/7
The entropy of a random variable X in bits is given by the formula:
H(X) = -∑P(X) log2(P(X))
Plugging in the probabilities above:
H(X) = -(1/3 log2(1/3) + 2/7 log2(2/7) + 4/7 log2(4/7))
H(X) = 1.585 bits
So, the entropy of the random variable X in this case is approximately 1.585 bits.
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katie has box of red ribbon and blue ribbon the ratio of red ribbon to toal is
I'm sorry, but you haven't provided enough information to determine the ratio of red ribbon to total. Please provide more details.
A food truck sells two types of meals: a hamburger for $5 and a
salad for $7. Yesterday, the food truck sold a total of 152 meals for a
total of $904.
Answer:
They sold 80 hamburgers and 72 salads.
Step-by-step explanation:
1) 72x7= 504
2) 80x5=400
3) 504+400=$904
The table shows how many heart beats per minute what is the unit rate in beats per minute
(HELP ASAP!)
Answer:
Below
Step-by-step explanation:
You are given beats (195) and minutes (3) and want beats/ minute
195 beats / 3 min = 65 beats per minute
260/4 = 65 beats/min
325 / 5 =65 beats/min
4. The quaternion group Q is a non-abelian group of order 8, whose elements are tradi- tionally written as Q = {1, i, j, k, -1, -i, -i, -k}, and which satisfy the following rules for multiplication: 1x = xl = x and (-1)x = x(-1) = = -x for x = 1, i, j, k (-1)2 = 1 i2 = j2 = k2 = ijk = -1 At this point, just take my word for it that a unique associative binary operation on Q exists satisfying these properties, and that this operation defines a group structure. (a) Compute the full 8 x 8 multiplication table for Q. (b) Find the inverses of all of the elements of Q. (c) Find the orders of all of the elements of Q. (d) Find the conjugacy classes of Q. (e) There are many ways to see that Q is not isomorphic to the dihedral group D4. State one.
Q is not isomorphic to the dihedral group D4 because the dihedral group D4 is abelian, while Q is not.
(a) The full 8 × 8 multiplication table for Q is as follows:
1 i j k -1 -i -j -k
1 i j k -1 -i -j -k
i -1 k -j -i 1 -k j
j -k -1 i -j k 1 -i
k j -i -1 -k -j i 1
-1 i j k 1 -i -j -k
-i -1 -k j i 1 k -j
-j k 1 -i j -k -1 i
-k -j i 1 k j -i -1
(b) The inverse of each element of Q is as follows:
1: 1
i: -i
j: -j
k: -k
-1: -1
-i: i
-j: j
-k: k
(c) The order of each element of Q is as follows:
1: 1
i: 4
j: 4
k: 4
-1: 2
-i: 4
-j: 4
-k: 4
(d) The conjugacy classes of Q are as follows:
{1}, {-1}, {i, -i}, {j, -j}, {k, -k}.
(e) One way to see that Q is not isomorphic to the dihedral group D4 is that the dihedral group D4 is abelian, while Q is not.
Q is not isomorphic to the dihedral group D4 because the dihedral group D4 is abelian, while Q is not.
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