Based on the calculations, the length of side CM is equal to 4 units.
How to calculate the length of side CM?First of all, we would determine the measure of angle B by applying the law of cosine as follows:
B² = A² + C² - 2(A)(C)cosB
Given the following data:
A = BC = 5
B = AC = 4√2
C = AB = 7
Substituting the given parameters into the formula, we have;
(4√(2))² = 5² + 7² - 2 × 5 × 7 × cosB
cos(B) = ((4√(2))² - (5² + 7²))/(-2×5×7)
cos(B) = 0.6
B = cos⁻¹(0.6)
B = 53.13°.
Now, we can find side CM by using sine trigonometry:
sin(B) = CM/BC
CM = BC × sin(B)
CM = 5 × sin(53.13°)
CM = 5 × 0.8
CM = 4 units.
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Diana earns $9.95 per hour
working at the bank. She
needs to save at least
9
$200.00 in 3 weeks.
Which inequality can be used
to determine h, the number of
hours she needs to work to
reach her goal?
Answer:
m = $9.00 * h.
Step-by-step explanation:
hours: 4, 5, 6, 7,
money: 34, 42.5, 51, 59.5,
help me
I need someone..
plsss..
Is -3x+5=-3x+8 infinate many solutions
PLSSS HELPP I SILL DO ANYTHZING
Answer:
well i don't know but i wish you the best of luck sorry always remember YOUR SMART ♥️♥️♥️♥️♥️
Step-by-step explanation:
There are 12 students in the gym class. If 4 students can sit on 1 bench, how many benches are needed for all students ?
Answer:
3 benches needed
Step-by-step explanation:
Answer:
3 benches
Step-by-step explanation:
4 people to one bench
12 people divided by 4 = 3 benches
please help please! -2/5x -9 < 9/10
Answer:
x>99/4
Step-by-step explanation: hope this helps :)
Plsss help meee :)))
Answer:
6*(-5)
Step-by-step explanation:
Answer:
6 times -5
Step-by-step explanation:
Use the image to answer the question. A coordinate plane with four quadrants shows the x- and y-axes ranging from negative 5 to 5 in increments of 1. A solid line and a dotted line intersect each other. The equation of the solid line is x minus 5 y equals 3. The equation of the dotted line is 3 x minus 2 y equals negative 4. The intersection of both lines is shown at negative 2 on the x-axis and negative 1 on the y-axis in quadrant 3.
Review the graphs of a system of two linear equations in two variables: x−5y=7 and 3x−2y=−4. Find the solution to both equations.(1 point)
The intersection point is ()
The equations given are x - 5y = 3 and 3x - 2y = -4. To find the solution to this system of equations, we need to find the values of x and y that satisfy both equations simultaneously.
Find the solution to both equations?One way to solve this system of equations is by substitution. We can solve one equation for x or y, and then substitute that expression into the other equation to eliminate one variable. Let's solve the first equation for x:
x - 5y = 3
x = 5y + 3
Now we can substitute this expression for x into the second equation:
3x - 2y = -4
3(5y + 3) - 2y = -4
15y + 9 - 2y = -4
13y = -13
y = -1
We can now substitute this value for y back into either equation to find the value of x:
x - 5y = 3
x - 5(-1) = 3
x + 5 = 3
x = -2
Therefore, the solution to the system of equations x - 5y = 3 and 3x - 2y = -4 is (-2, -1). This is the point where the solid line and dotted line intersect, as shown in the image.
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Prove that if a1,a2,a3∈R,a1,a2,a3=0 and {v1,v2,v3} is a linearly independent set of vectors then so is {a1v1,a2v2,a3v3}.
It is proved that {a₁v₁, a₂v₂, a₃v₃} is linearly independent.
Here, we have,
To prove that the set {a₁v₁, a₂v₂, a₃v₃} is linearly independent given that {v₁, v₂, v₃} is a linearly independent set, we need to show that the only linear combination of a₁v₁, a₂v₂, and a₃v₃ that equals the zero vector is the trivial combination where the coefficients are all zero.
Let's assume that there exist scalars b₁, b₂, and b₃, not all equal to zero, such that:
b₁(a₁v₁) + b₂(a₂v₂) + b₃(a₃v₃) = 0
Expanding this equation, we have:
a₁b₁v₁ + a₂b₂v₂ + a₃b₃v₃ = 0
Since {v₁, v₂, v₃} is linearly independent, the only way for this equation to hold is if a₁b₁ = a₂b₂ = a₃b₃ = 0.
Since a₁, a₂, a₃ are nonzero and b₁, b₂, b₃ are not all zero, we can conclude that a₁b₁ = a₂b₂ = a₃b₃ = 0 if and only if b₁ = b₂ = b₃ = 0.
Therefore, the only linear combination of a₁v₁, a₂v₂, and a₃v₃ that equals the zero vector is the trivial combination, where b₁ = b₂ = b₃ = 0.
Hence, {a₁v₁, a₂v₂, a₃v₃} is linearly independent.
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Please help due today
Computers depreciate rapidly. If a new computer that costs $1200 loses 40% of its value every year, what is its worth 5 years from now?
Answer:
93.312
Step-by-step explanation:
This would be decay so we use the formula \(y=a(1-r)^{2}\)
in this case a would equal $1200, r would equal 40% (as a decimal) or 0.4 and x would equal 5
\(y=1200(1-0.4)^5\) plug this into your calculator and you will get 93.312
I hope this helps (Lmk if im wrong )
Based on the mass and volumes of each crown below, which crown do you think is densest?
Saturn has the densest crown based on Gizmo densities, with a density of 687 kg/m³.
What is density?The density of an item is calculated theoretically as its mass divided by its volume.
The weight of an object is defined as its mass. The volume of a thing is the amount of space that the object or substance takes up.
As a result, density refers to the ratio or numerical connection between an object's mass and the quantity of space it occupies.
Saturn is the densest planet in terms of both mass and volume. Saturn is denser than a rock, quarter, cruise ship, or beach ball, according to what we can see from the Gizmos.
See the table below for their densities.
Objects Relative Density
Rock 2.6g/cc³
Cruise Ship 9.0g/cm³
Quarter 8.9 g/ml³
Saturn 687 kg/m³
Beach ball 10 g/cc³
Thus, we selected Saturn as the Gizmo with the densest crown.
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Since the area of the circle is startfraction pi over 4 endfraction the area of the square, the volume of the cone equals startfraction pi over 4 endfraction the volume of the pyramid or startfraction pi over 4 endfractionstartfraction pi over 4 endfraction (startfraction (2 r) (h) over 3 endfraction) or one-sixthπrh. startfraction pi over 4 endfraction the volume of the pyramid or startfraction pi over 4 endfractionstartfraction pi over 4 endfraction (startfraction (2 r) squared (h) over 3 endfraction) or one-thirdπr2h. startfraction pi over 2 endfraction the volume of the pyramid or startfraction pi over 2 endfraction or two-thirdsπr2h. startfraction pi over 2 endfraction the volume of the pyramid or startfraction pi over 4 endfraction or one-thirdπr2h.
The volume of the cone is one-third the volume of the pyramid, the area of the circle is pi/4 the area of the square because the radius of the circle is half the side length of the square.
The volume of the cone is one-third the volume of the pyramid because the cone's base is a sector of the square, and the sector takes up one-third of the square's area.
Volume of a cone: The volume of a cone is equal to (1/3)πr²h, where r is the radius of the base and h is the height of the cone.
Volume of a pyramid: The volume of a pyramid is equal to (1/3)Bh, where B is the area of the base and h is the height of the pyramid.
In the problem, we are told that the area of the circle is pi/4 the area of the square. This means that the radius of the circle is half the side length of the square. We can use this information to find the volume of the cone and the pyramid.
Volume of the cone: The radius of the cone is half the side length of the square, so r = s/2. The height of the cone is h. The area of the base of the cone is (pi)(r²) = (pi)(s²/4). So, the volume of the cone is (1/3)π(s²/4)h = (1/12)πs²h.
Volume of the pyramid: The area of the base of the pyramid is the same as the area of the base of the cone, which is (pi)(s²/4). The height of the pyramid is the same as the height of the cone, which is h. So, the volume of the pyramid is (1/3)π(s²/4)h = (1/12)πs²h.
As you can see, the volume of the cone is equal to one-third the volume of the pyramid.
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Match each value of r to its scatterplot: Data 100 09 09 GRAPHA OP 8 3 40 8 0 100 Det 001 OH 0 GRAPH B OP 30 100 Duta 00 GRAPH C 爱 arch Data 100 80 60 OOO GRAPHD 20 0 0 20 40 80 100 Data 100 80 09 OOOOOOOOOOOOOOOO GRAPHE ON OZ 0 0 20 40 50 09 100 A [Choose B [ Choose -1 0.373 -0.908 0.881 -0.732 [ Choose C > D [ Choose E [Choose ]
Graphs and the correlation coefficients are mentioned below-
Graph{A} : 0.373Graph{B} : - 0.908Graph{C} : - 0.732Graph{D} : 0.881Graph{E} : - 1What is Scatter plot?
A scatter plot uses dots to represent values for two different numeric variables. There are three types of scatter plots or charts -
U-shapedlinear exponential.There are the three most important correlations as -
positive correlationnegative correlationno correlationGiven are the scatter plots and the associated correlation coefficient.
Correlation coefficient : it is a measure of linear correlation between two sets of data. Mathematically, we can write -\($r =\frac{\sum\left(x_{i}-\bar{x}\right)\left(y_{i}-\bar{y}\right)}{\sqrt{\sum\left(x_{i}-\bar{x}\right)^{2} \sum\left(y_{i}-\bar{y}\right)^{2}}}\)
r = correlation coefficient
\($x_{i}\) = values of the x-variable in a sample
\($\bar x\) = mean of the values of the x-variable
\($y_{i}\) = values of the y-variable in a sample
\(\bar y\) = mean of the values of the y-variable
The graph and their corresponding values of [r] are mentioned below -
Graph{A} : 0.373Graph{B} : - 0.908Graph{C} : - 0.732Graph{D} : 0.881Graph{E} : - 1Therefore, graphs and the correlation coefficients are mentioned below-
Graph{A} : 0.373Graph{B} : - 0.908Graph{C} : - 0.732Graph{D} : 0.881Graph{E} : - 1To solve more questions on scatter plots, visit the link below-
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What is 235°, expressed in radian measure
A.235 π
B. π/235
C.36 π/47
D.47 π/36
Answer:
it's A hope this helps
Step-by-step explanation:
sorry if it's wrong but I think it's correct in shaa Allah
Im confused right now. What equasion is represented by the area model? Format as 2x2
40x30=120x5=600x6=3600
Awnser:3600
A particular jury consists of 7 jurors. Each juror has a 0. 2 chance of making the wrong decision, independently of the others. If the jury reaches a decision by majority rule, what is the probability that it will reach a wrong decision?.
The probability that the jury will make a wrong decision is 0.033
The number of jury that makes the wrong decision can be modeled as a binomial random with parameters n=7 and p=0.2. This jury as a whole will make wrong decision if 4, 5, 6, or 7 make the wrong decision.
Now, denote the events with A, B, C, D for 4, 5, 6, 7 respectively. The probability of this union is the sum of probabilities, so that:
P(Jury Error) = P(A)+P(B)+P(C)+P(D)
\(\left \ ({{7} \atop {4}} \right.)(0.2)^{4} *(0.8)^{3}+\left \(( {{7} \atop {5}} \right. )(0.2)^{5} *(0.8)^{2} +\left \ ({{7} \atop {6}} \right.)(0.2)^{6} *(0.8)^{1} +\left \(( {{7} \atop {7}} \right.)(0.2)^{7} *(0.8)^{0}\)
\(=0.033\)
\(P(Jury Error)=0.033\)
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of the 900 students at columbia middle school, there are 324 7th graders. If one student is chosen at random to lead the pledge at a school assembly, what is the probability the person chosen will be a 7th grader? Use prime factorization to reduce the answer.
Answer:
Step-by-step explanation:
im am sorry but i dont understand so i cant answer this question see you later!
Show how to use a property of arithmetic to make the addition problem 997+543 easy to calculate mentally. Write equations to show your use of a property of arithmetic. State the property you use and show where you use it.
By using the associative property of addition, we can break down the addition problem 997 + 543 into smaller, more manageable calculations.
The associative property of addition states that the grouping of numbers being added does not affect the result. In other words, (a + b) + c is equal to a + (b + c).
To make the mental calculation easier for 997 + 543, we can break down the numbers into smaller parts. Let's split 543 into 500 and 43:
997 + (500 + 43)
Now, we can calculate the addition in two steps:
Step 1: Add 500 and 43:
(997 + 500) + 43
Step 2: Add the results together:
1497 + 43
Calculating this mentally:
1497 + 43 = 1540
By utilizing the associative property of addition, we broke down the numbers into smaller parts and performed the addition in multiple steps. The sum of 997 + 543 is equal to 1540. This approach simplifies the mental calculation by breaking it down into manageable chunks.
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A prescription for Singulair costs $14 for a month's supply. How much will this prescription cost for a year?
PLS HELP HW DUE IN 2MIN!!!!
When the point (5, 5) is transformed using a translation, the result is point ( -1, 11). Complete the function below.
Answer: (x,y) = (-6, 6)
Step-by-step explanation: I'm not very good at explaining but if you you follow this equation, (x1-x2, y1-y2) with (x1,y1) (5,5) and (x2,y2) being the function, that's how you get (-1,11)
Please Answer this Hurry!
Answer:
hope this helps
Step-by-step explanation:
Solve the circled questions (I solved a few of them not exactly sure if they are correct).
The equation "tan(⍉)• cos(⍉)=sin(⍉)" is true for all values of ⍉.
The equation "(1 - cos ⍉)(1 - cos ⍉) = sin (⍉)" is true for all values of ⍉.
The equation "(1 + sin ⍉)(1 - sin ⍉) = cos ² (⍉)" is true for all values of ⍉.
How did we get the assertions?To prove the equation "tan(⍉)• cos(⍉)=sin(⍉)", we can use the identity:
tan(⍉) = sin(⍉) / cos(⍉)
Therefore, tan(⍉)• cos(⍉) = (sin(⍉) / cos(⍉)) * cos(⍉) = sin(⍉).
To prove the equation "(1 - cos ⍉)(1 - cos ⍉) = sin (⍉)", we can use the identity:
cos²(⍉) = 1 - sin²(⍉)
So, (1 - cos ⍉) = √(1 - cos²(⍉)) = sin(⍉), and
(1 - cos ⍉)(1 - cos ⍉) = sin²(⍉) = sin (⍉).
To prove the equation "(1 + sin ⍉)(1 - sin ⍉) = cos ² (⍉)", we can use the identity:
cos²(⍉) = (1 + cos(⍉)) / 2
and
sin²(⍉) = (1 - cos(⍉)) / 2
Therefore, (1 + sin ⍉)(1 - sin ⍉) = (1 + (1 - cos(⍉)) / 2) * (1 - (1 - cos(⍉)) / 2) = (1 + (1 - cos(⍉)) / 2) * (1 + cos(⍉) / 2) = (2 + cos(⍉)) / 2 = cos²(⍉).
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A hop ha a ale that offer 20% of all price. On the final day they reduce all the ale price by 25%. Linz buy a radio on the final day. Work out the overall percentage reduction on the price of the radio.
the customer saved 45% on the price of the radio compared to the original price.
25%
The original price of the radio = 100%
The 20% discount = 100%-20% = 80%
The 25% discount = 80%-25% = 55%
Overall percentage reduction = 100%-55% = 45%.
The original price of the radio was 100%. On the final day, the ale was discounted by 25%, which reduced the price to 80%. This was then further discounted by 20%, bringing the price to 55%. Therefore, the overall percentage reduction on the price of the radio was 45%. This means that the customer saved 45% on the price of the radio compared to the original price.
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Someone help me out with this need a quick respond
what is the median of these numbers 17 12 54 36 71 28 31 55
Answer:
The median is 33.5
Step-by-step explanation:
In order to solve for a median it would either be the middle or it would be the average of the middle if there are even amount of numbers. First you would put them in order. 12 17 28 31 36 54 55 and 71. This would mean the the middle number would be 31 and 36. Since you can't have two medians you would find the average of the two so add 31 and 36 which would be equal to 67 then divide by 2 which would equal to 33.5.
The median of numbers 17, 12, 54, 36, 71, 28, 31, 55 is 33.5.
What is the median of a set of numbers?The median of a set of numbers is the middle value when the numbers are arranged in ascending or descending order.
If there are an even number of numbers, the median is the average of the two middle values. If there is an odd number of numbers, the median is the middle number.
To find the median of the given numbers, we first need to arrange them in ascending order:
12 17 28 31 36 54 55 71
Since there are an even number of numbers (8), the median will be the average of the two middle values, which are 31 and 36.
To find the average, we add the two numbers and divide by 2:
(31 + 36) / 2 = 67 / 2 = 33.5
Therefore, the median of the given numbers is 33.5.
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Which function is graphed?
A f(x)=−2x
B f(x)=−x21
C f(x)=x21
D f(x)=2x
Answer:
A is the correct answer
Linda walked a total of 2614 miles during a 4-day period. The distances she walked on the first 3 days are described below. She walked 613 miles the first day. On the second day, she walked 912 miles. She walked 514 miles on the third day. How far did she walk on the fourth day?
Answer: She walked 575 miles on the fourth day.
Step-by-step explanation: 2614-613-912-514= 575
a. (5) The demand function for a good X is Qx= m-3Px+2Py, where m is income, Px is the price of X, Py is the price of a related good Y and Qx is the demand for X. Income and prices are all positive. X
The demand function for good X is Qx = m - 3Px + 2Py, where Qx is the quantity demanded of X, m is income, Px is the price of X, and Py is the price of a related good Y. The equation shows that the demand for X is inversely related to its price and directly related to the price of Y. Income, price of X, and price of Y collectively affect the overall demand for X.
The demand function for good X is given by Qx = m - 3Px + 2Py, where Qx represents the quantity demanded of good X, m is the income, Px is the price of good X, and Py is the price of a related good Y. In this equation, the income and prices are assumed to be positive.
To determine the demand for good X, we can analyze the equation. The coefficient -3 in front of Px indicates that the demand for good X is inversely related to its price. As the price of X increases, the quantity demanded of X decreases, assuming other factors remain constant. On the other hand, the coefficient 2 in front of Py indicates that the demand for good X is directly related to the price of the related good Y. If the price of Y increases, the quantity demanded of X also increases, assuming other factors remain constant.
Furthermore, the term (m - 3Px + 2Py) represents the overall effect of income, price of X, and price of Y on the quantity demanded of X. If income (m) increases, the quantity demanded of X increases. If the price of X (Px) increases, the quantity demanded of X decreases. If the price of Y (Py) increases, the quantity demanded of X increases.
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What is the probability that a randomly selected day from 2013 will have fewer than 2,740,000 group trades?
The probability that a randomly selected day will have a group trades total within 85,000 of the mean is 0.1328.
What is the probability about?
In the question given, the Mean (u) is said to be = 3421439
Therefore since Standard deviation = 508638.08
Note that:
z = x-u/sd
So:
P(u - 85000 <= x <= u + 85000)
u = 3421439
We insert the formula into the equation and it will be
= P(3421439 - 85000, 3421439 + 85000)
= P(3336439, 3506439)
= (3336439 - 3421439) / 508638.08, 3506439-3421439) / 508638.08)
= prob(-0.1671 and 0.1671 (So check the column under the z table)
So:
= 0.5664 - 0.4336
= 0.1328
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