What is the area of this figure?
You can split thus shape into 3 different rectangles.
The bottom rectangles area can be calculated using Base x Height
So 8 x 12 = 96cm²
The middle triangle is a little more difficult. but all you need to do is find the base to do base times height. You do this by doing 8 - 4 (because the length below it is 8 and you just minus 4)
8-4 = 4
So now you do 4 x height (5)
20cm²
Third top rectangle now.
Look at the bottom length and just minus that by 4 and 2 because if you imagine the bottom length coming up you can see it would be cut off.
So 8 -4 -2 = 2
The bottom is 2 (we know this is correct as the top length is also 2)
Base x Height
2 x 6 = 12cm²
Now add all the area together
96 + 20 + 12 = 128cm²
find the area of the shape below 11cm 14cm 20cm 9cm
Answer:202.5
Step-by-step explanation:
S1=(9*5)/2=22.5
S2=(20*9)=180
S=S1+S2=22.5+180=202.5
a circular pool is surrounded by a brick walkway 3 m wide. find the ra- dius of the pool if the area of the walk- way is 198 m*.
The radius of the pool is 9.01 m.
Given,
In the question:
A circular pool is surrounded by a brick walkway 3 m wide.
The area of the walk- way is 198 m^2.
To find the Radius of the pool.
Now, According to the question:
"Area of the circle bounded by the outside edge of the walkway" minus "area of the pool" = "area of the walkway".
Let R = Radius of the pool
Area of the circle bounded by the outside edge of the walkway is:
\(\pi\)(R +3)^2
Area of the pool is:
\(\pi R^2\)
Now, Our equation is:;
\(\pi\)(R +3)^2 - \(\pi R^2\) = 198
\(\pi\)((R+3)^2 - \(R^2\)) = 198
Open the inner bracket :
\(\pi\)(\(R^2+6R+9-R^2\)) = 198
\(\pi\)(6R +9) = 198
6R+9 = 198/\(\pi\)
6R = 198/\(\pi\) - 9
R = (198/\(\pi\) - 9)/6
R = (198/(3.14) - 9)/6
R = (63.057 - 9)/6
R = 54.057/6
R = 9.01 meters
Hence, The radius of the pool is 9.01 m.
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Evaluate the expression (3 • 2)^2
Answer:
36
Step-by-step explanation:
(3*2)^2
3*2=6
6^2=36
Answer:
36
Step-by-step explanation:
(3x2)^2
6^2
36
Hopes this helps please mark brainliest
Simplify (x + 3)2 + 4
Answer:
2x+10
Step-by-step explanation: First you have to distribute the two, into the parenthesis. Which brings it to 2x+6+4 and then you just combine the 6 and 4 making it a ten so 2x+10
help please
A family has a unique pattern in their tile flooring on the patio. An image of one of the tiles is shown.
A quadrilateral with a line segment drawn from the bottom vertex and perpendicular to the top that is 5 centimeters. The right vertical side is labeled 3 centimeters. The portion of the top from the left vertex to the perpendicular segment is 5 centimeters. There is a horizontal segment from the left side that intersects the perpendicular vertical line segment and is labeled 6 centimeters.
What is the area of the tile shown?
53 cm2
45.5 cm2
42.5 cm2
36.5 cm2
The area of the tile shown is C) 42.5 cm².
To calculate the area of the tile shown, we need to divide it into two triangles and a rectangle. The rectangle's area is the product of the length and width, which is 3 cm x 6 cm = 18 cm².
To find the area of the triangles, we need to use the formula for the area of a triangle, which is 1/2(base x height). The base and height of the left triangle are 5 cm and 6 cm, respectively. So, the area of the left triangle is 1/2(5 cm x 6 cm) = 15 cm².
The base and height of the right triangle are 3 cm and 5 cm, respectively. So, the area of the right triangle is 1/2(3 cm x 5 cm) = 7.5 cm².
Adding the areas of the rectangle and the two triangles, we get 18 cm² + 15 cm² + 7.5 cm² = 40.5 cm². Therefore, the area of the tile shown is 40.5 cm², which is closest to the option C, 42.5 cm².
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Subtract (-9x + 3y) from (-2x - y): 4y-7x O-11x + 2y O-7x-4y 7x+2y 7x - 4y
The correct subtraction of (-9x + 3y) from (-2x - y) results in the expression 7x - 4y. Therefore, the correct answer is 7x - 4y.
To understand why this is the correct answer, let's break down the process of subtracting (-9x + 3y) from (-2x - y). When subtracting a term, say A, from another term, say B, we can rewrite the subtraction as the addition of the opposite of A. In this case, we are subtracting (-9x + 3y), so we can rewrite it as the addition of (9x - 3y). Now, we have (-2x - y) + (9x - 3y). To simplify this expression, we combine like terms. The x terms give us -2x + 9x, which equals 7x. The y terms give us -y - 3y, which equals -4y. Therefore, the final result is 7x - 4y.
In conclusion, when subtracting (-9x + 3y) from (-2x - y), the correct answer is 7x - 4y.
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Dance class has 22 students; 10 are women and 12 are men. if5 men and 5 women are tobe chosen and then paired off, how many results are possible?
A total of 23, 950, 080 results are possible.
We are given;
10 women
12 men
5 men and 5 women, chosen and pared off, how many results in total?
Thus;
[10 choose 5] x [12 choose 5]=252 x 792 = 199584 ways
We then need to know how many ways there could put into pairs i.e. For the first woman, there will be 5 choices of men. For the second woman, there will be 4 choices remaining of men. For the third woman, there will be 3 choices remaining. For the fourth woman, there will be only 2choices remaining, and only 1 choice left for the last woman.
Therefore, there are 5x4x3x2x1 = 120 ways.
In total there are 199584x120 = 23950080 total ways
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Alex can run 26 miles in 6 hours, Bethany can run 26 miles in 5 hours and Carol can run 26 miles in 4 hours. If they start together and each run at their constant speeds, how many hours does it take for them to finish a total of 26 miles among the three of them
It takes approximately 86.67 hours for Alex, Bethany, and Carol to collectively finish a total of 26 miles. This is determined by calculating the harmonic mean of their individual running speeds.
To determine how many hours it takes for Alex, Bethany, and Carol to collectively run a total of 26 miles, we need to consider their individual running speeds. Alex runs at a rate of 26 miles in 6 hours, Bethany runs at a rate of 26 miles in 5 hours, and Carol runs at a rate of 26 miles in 4 hours.
To find the total time it takes for them to finish 26 miles together, we can calculate the harmonic mean of their individual running speeds. The harmonic mean is used because it accounts for the different rates at which they run.
The formula for the harmonic mean is given by:
Harmonic Mean = Total Distance / (1 / Speed1 + 1 / Speed2 + 1 / Speed3)
Substituting the values, we have:
Harmonic Mean = 26 / (1 / 6 + 1 / 5 + 1 / 4)
To simplify the equation, we find the common denominator:
Harmonic Mean = 26 / ((5 + 6 + 7) / 60)
Harmonic Mean = 26 / (18 / 60)
Harmonic Mean = 26 / (3 / 10)
Harmonic Mean = 26 * (10 / 3)
Harmonic Mean ≈ 86.67
Therefore, it takes approximately 86.67 hours for Alex, Bethany, and Carol to collectively finish a total of 26 miles.
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Solve |7x + 21| = 14x. Identify the solution and an extraneous solution.
Answer:
Step-by-step explanation:
solution: x=3;
extraneous solution: x=-1
The solution is 3 and the extraneous solution is -1.
What is the modulus function?The modulus function is the function which gives the magnitude or absolute of the number in the variable.
|x|=x if x>0
-x if x<0
0 if x=0
So according to question,
|7x+21|=14x
case-1: if 7x+21>0
⇒7x>-21
⇒x>-21/7
⇒x>-3
if 7x+21>0 , Using the modulus function property
|7x+21|=14x
⇒7x+21=14x
⇒14x-7x=21
⇒7x=21
⇒x=21/7
⇒x=3 which is also x>-3
x=3 is the solution
case-2: if 7x+21<0
⇒7x<-21
⇒x<-21/7
⇒x<-3
if 7x+21<0 , Using the modulus function property
|7x+21|=14x
⇒-(7x+21)=14x
⇒-7x-21=14x
⇒14x+7x=-21
⇒21x=-21
⇒x=-21/21
⇒x=-1 for which x<-3 is not true
x=-1 is an extraneous solution.
Therefore the solution is 3 and the extraneous solution is -1.
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According to the reading, good measures are...
(select as many as apply)
Mark all that apply
robust
easily obtainable
transferable
secure
valid
objective
simple
quickly comprehensible
precisely definable
Good measures are robust, valid, objective, simple, and precisely definable.
In the context of measurement, good measures possess certain qualities that make them reliable and useful. Based on the options provided, the following qualities apply:
Robust: Good measures are robust, meaning they are resistant to outliers or extreme values that may affect the accuracy of the measurement.
Valid: Good measures are valid, meaning they accurately measure what they are intended to measure and provide meaningful information.
Objective: Good measures are objective, meaning they are free from bias or subjective interpretation, ensuring consistency and fairness.
Simple: Good measures are simple, making them easy to understand and apply. They avoid unnecessary complexity and confusion.
Precisely definable: Good measures have clear and precise definitions, ensuring consistent interpretation and allowing for replication in different contexts.
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Complete the transformations below. Then enter the final coordinates of the figure.
A" (,)
B" (,)
C" (,)
HELP! PLZ.
Answer:
Step-by-step explanation:
If a point (x, y) is translated by 4 units horizontally right and 1 unit upwards, coordinates of the image point will be,
(x, y) → (x + 4. y + 1)
Therefore, vertices of the image triangle ABC will be,
A(2, 2) → A'(2+4, 2+1)
→ A'(6, 3)
B(5, -1) → B'(5+4, -1+1)
→ B'(9, 0)
C(1, -2) → C'(1+4, -2+1)
→ C'(5, -1)
Then reflected across y-axis.
Rule for the reflection across y-axis will be,
(x, y) → (-x, y)
A'(6, 3) → A"(-6, 3)
B'(9, 0) → B"(-9, 0)
C'(5, -1) → C"(-5, -1)
Answer:
A"(-6, 3)
B"(-9, 0)
C"(-5, -1)
Step-by-step explanation:
is (-1 ,-5) a solution to the inequality 4x+y<-3
The expression (-1 ,-5) is not a solution to the inequality 4x + y < -3
How to determine if (-1 ,-5) is a solution to the inequality 4x + y < -3?The inequality is given as
4x + y < -3
The solution is given as
(-1, 5)
Substitiute (-1, 5) for (x, y) in the inequality expression 4x + y < -3
So, we have
4(-1) + 5 < -3
Open the bracket
-4 + 5 < -3
Evaluate the sum
1 < -3
The above inequality is false
Hence, (-1 ,-5) is not a solution to the inequality 4x + y < -3
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is 10x-5=8x-2x + 7 -2 equivalent?
Answer:
2.5
Step-by-step explanation:
Lets simpify one side first
8x - 2x + 7 +2
8-2 = 6
so 6x
7-2 = 5
6x+9
10x - 5 = 6x +5
(You add 5 due to it being negative on the other side)
+5 +5
10x= 6x +10
-6x -6x
4x = 10
Divide each side by 4
x = 2.5 or 10/4 or 5/2
Answer: No
Step-by-step explanation: To find whether these are equivalent, we first need to simplify the equation on the right.
8x-2x+7-2
8x-2x+5 (work- 7-2 = 5)
6x+5 (work- 8x-2x=6x) These are like terms, so we can subtract them
now that we have simplified, let's write the equations once again.
10x-5=6x+5
they are surely not equivalent
How I can answer this question, NO LINKS, if you answer correctly I will give u brainliest!
Answer:
A) -12 x 10^9
Step-by-step explanation:
\(\frac{5}{6}x - 8=\frac{1}{3}(3x-15)\)
Answer:
x= -18
Step-by-step explanation:
Solve for
x
by simplifying both sides of the equation, then isolating the variable.
Choose the best graph that represents the linear equation:
6x = y + 8
Graph A
On a coordinate plane, a line goes through (negative 2, 4) and (0, negative 8).
Graph B
On a coordinate plane, a line goes through (0, negative 8) and (2, 4).
Graph C
On a coordinate plane, a line goes through (negative 2, negative 4) and (0, 8).
Graph D
On a coordinate plane, a line goes through (0, 8) and (2, negative 4).
a.
Graph A
c.
Graph C
b.
Graph B
d.
Graph D
use an inverse matrix to solve the system of linear equations. 5x1 4x2 = 7 −x1 x2 = −23
The solution to the system of linear equations using an inverse matrix is x1 = 161/9 and x2 = -112/9.
To solve the system of linear equations using an inverse matrix, we can represent the system in matrix form as follows:
```
[ 5 4 ] [ x1 ] [ 7 ]
[-1 1 ] [ x2 ] = [ -23 ]
```
Let's denote the coefficient matrix as A, the variable matrix as X, and the constant matrix as B. We can rewrite the equation as AX = B.
```
A = [ 5 4 ]
[-1 1 ]
X = [ x1 ]
[ x2 ]
B = [ 7 ]
[ -23 ]
```
To solve for X, we can use the formula X = A^(-1) * B, where A^(-1) represents the inverse of matrix A.
First, let's calculate the inverse of matrix A:
```
A^(-1) = (1 / determinant(A)) * adjoint(A)
```
The determinant of A is: (5 * 1) - (4 * -1) = 9
The adjoint of A is:
```
[ 1 -4 ]
[ -1 5 ]
```
Therefore, the inverse of A is:
```
A^(-1) = (1/9) * [ 1 -4 ]
[ -1 5 ]
```
Now, we can calculate X:
```
X = A^(-1) * B
```
Substituting the values:
```
X = (1/9) * [ 1 -4 ] * [ 7 ]
[ -1 5 ] [ -23 ]
```
Calculating the matrix multiplication:
```
X = (1/9) * [ (1*7 + -4*-23) ]
[ (-1*7 + 5*-23) ]
```
Simplifying the calculations:
```
X = (1/9) * [ 161 ]
[ -112 ]
```
Therefore, the solution to the system of linear equations is:
```
x1 = 161/9
x2 = -112/9
```
Hence, the solution to the system of linear equations using an inverse matrix is x1 = 161/9 and x2 = -112/9.
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multiplying and dividing rational numbers word problems.....I have a test tomorrow so I need all the help I could get
Multiplication
\(\frac{3}{4}\times\frac{8}{3}\)you multiply the numbers that are in front
\(\begin{gathered} \frac{3\times8}{4\times3} \\ \\ \frac{24}{12} \end{gathered}\)then simplify and the answer is 2
Division
\(\frac{\frac{3}{4}}{\frac{8}{3}}\)
you multiply the extremes and the solution is the numerator of the result
then multiply the internals and the solution is the denominator of the result
\(\begin{gathered} \frac{3\times3}{4\times8} \\ \\ \frac{9}{32} \end{gathered}\)Other exercise about division
so the solution is
\(\frac{12}{2}=6\)if you run for 30 mintes at a speed of 8 miles per hour how many feet wpuld you hav erun
Answer:
not sure if this is correct but i tried (1267200 feet)
Answer:
21120 ft
Step-by-step explanation:
We need to change 8 miles per hour to feet per minute
8 miles 5280 ft 1 hour
----------- * ---------- * ----------
hour 1 mile 60 minutes
704 ft/ minute
Now multiply by 30 minutes
704 ft / minute * 30 minutes =21120 ft
A Set of Speakers costs $35 and Songs cost $195 each. The sales tax
rate is 8.25%. The expression 0.0825(35+ 195s) can be used to determine
the amount of sales tax due on the entire purchase of a set of Speakers
and S.Songs. Expand the expression and round to the nearest hundredth.
The amount of sales tax due on the entire purchase of a set of speakers and s songs is given by expression 2.8875+16s
What is an expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given that :
Cost of speaker = $35
Cost per song = $195
Sales tax rate = 8.25%
Expression to obtain the amount of sales tax on entire purchase : 0.0825(35+ 195s)
Using distributive law to expand the expression :
0.0825(35+ 195s)
= 2.8875+16s
Hence, the amount of sales tax due on the entire purchase of a set of speakers and s songs is given by expression 2.8875+16s
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can someone who took the test please help me out
The graph of the following coordinates can be graphed by plotting the points of given coordinates on the graph.
What are coordinates?Coordinates are a pair of integers (also known as Cartesian coordinates), or occasionally a letter and a number, that identify a specific point on a grid, also known as a coordinate plane.
What is a point?A point is a dot on a sheet of paper or in a plane. There are no lengths, widths, or heights in a point. It establishes a plane's position or location.
Plot the points according to the given coordinates. Connect all the points with with a smooth curve.
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hat is the variance of the number of fixed elements, that is, elements left in the same position, of a randomly selected permutation of n elements? [hint: let x denote the number of fixed points of a random permutation. write x
Let X be the number of fixed points of a random permutation of n elements. A fixed point is an element that remains in the same position after the permutation. Thus, the probability that an element is fixed is 1/n, and the probability that it is not fixed is (n-1)/n.
Using the linearity of the expected value, we can calculate the expected value of X as:
E(X) = E(X1 + X2 + ... + Xn) = E(X1) + E(X2) + ... + E(Xn)
where Xi is the indicator random variable that is equal to 1 if the i-th element is fixed and 0 otherwise. Since the probability of an element being fixed is 1/n, we have E(Xi) = 1/n. Therefore,
E(X) = n * (1/n) = 1
To find the variance of X, we need to compute E(X^2) - E(X)^2. We can use the fact that X^2 = X1 + X2 + ... + Xn, where Xi is the indicator random variable that is equal to 1 if the i-th and j-th elements are both fixed and 0 otherwise. Then,
E(X^2) = E(X1 + X2 + ... + Xn)^2 = E(X1^2 + X2^2 + ... + Xn^2) + 2 E(X1X2 + X1X3 + ... + X(n-1)n)
Since there is only one way to fix two elements out of n, we have E(XiXj) = 1/(n(n-1)). Therefore,
E(X^2) = n * (1/n) + n(n-1) * (1/(n(n-1))) = 1 + 1/n
Finally, the variance of X is
Var(X) = E(X^2) - E(X)^2 = 1 + 1/n - 1^2 = 1/n
Therefore, the variance of the number of fixed elements of a randomly selected permutation of n elements is 1/n.
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Which algebraic expression would be used to denote a trisomic organism? a. 1n b. 3n c. 2n - 1 d. 2n + 1 e. 2n + 2.
The correct answer to the given question is d. 2n+1. The other options, such as 1n, 3n, 2n-1, and 2n+2, do not accurately represent the chromosome number of a trisomic organism.
A trisomic organism is one that has an extra copy of a chromosome in its genome. This means that it has three copies of a particular chromosome instead of the usual two, which can have significant implications for the organism's development and health.
In terms of algebraic notation, the chromosome number of a trisomic organism would be denoted as 2n+1, where "n" represents the normal diploid number of chromosomes for that organism. The "2n" represents the normal two sets of chromosomes, and the "+1" represents the extra chromosome.
Therefore, the correct answer to the given question is d. 2n+1. The other options, such as 1n, 3n, 2n-1, and 2n+2, do not accurately represent the chromosome number of a trisomic organism. It is important to note that trisomies can occur for any chromosome, not just the sex chromosomes, and can have varying effects depending on which chromosome is affected.
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Sheldon can either take a train or an airplane to San Francisco. If the train takes 11 hours and 23 minutes and the plane takes 2 hours and 44 minutes, how much time would he save taking an airplane? ( __ hours & __ minutes)
Sheldon can either take a train or an airplane to San Francisco. If the train takes 11 hours and 23 minutes and the plane takes 2 hours and 44 minutes, how much time would he save taking an airplane? ( __ hours & __ minutes)
Answer: he would save (9) hours (44) minutes on an airplane.
Step-by-step explanation: its easy just subtract 11 &2 & you'll get 9 hours but you don't do anything with the 44 & 23 all you have to do is put down 9 - hours & 44 - minutes. it's a piece of cakeplease rate me with 5 stars & thank me & hit the little crown please and thank you and if you want to be friends we can just friend me please and thank you and your welcome!!!!
a number is multiplied by 7 then 2.5 is added the result is 58.5
Answer:
The number is 8
Step-by-step explanation:
You subtract 2.5 from 58.5 which would be 56 and divided that by 7 which would give you he number 8.
on a coordinate plane, which point lies on the y-axis? question 2 options: (9,9) (9,0) (0,9) (-9,-9)
On the coordinate plane , the point which lies on the y -axis is given by option ( 0 , 9 ).
As given in the question,
On the coordinate plane :
Point which lies on the y - axis is given by :
a. ( 9 , 9 )
This coordinate lies in the first quadrant. It will not lies on any of the axis.
False.
b. ( 9 , 0 )
In this coordinate has y-,coordinate is equal to zero , it lies on the x- axis.
False.
c. ( 0 , 9 )
In this coordinate has x-,coordinate is equal to zero , it lies on the y- axis.
True.
d. ( -9 ,-9 )
This coordinate lies in the third quadrant. It will not lies on any of the axis.
False.
Therefore, on the coordinate plane the point that lies on the y-axis is
( 0, 9).
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Broo please help me omg
Answer:
9. -2
10. 0
Step-by-step explanation:
It is not undefined because the slope of horizontal lines are 0
What is ""statistical conclusion validity""? what was the main threat to statistical conclusion validity discussed in class?
Statistical conclusion validity is the extent to which inferences and conclusions drawn from statistical data are valid.
The main threat to statistical conclusion validity discussed in class is the potential for spurious correlations. This is when two variables appear to be related when in fact they are not.
Statistical conclusion validity is a measure of how valid the conclusions drawn from statistical data are. This is important because it allows us to draw valid inferences from the data. The main threat to statistical conclusion validity discussed in class is the potential for spurious correlations. This is when two variables appear to be related when in fact they are not. For example, a study may show that there is a correlation between ice cream sales and crime rate, when in fact it is merely a coincidence that both variables increase during the summer months. By controlling for other variables and using appropriate statistical tests, it is possible to identify and avoid spurious correlations.
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Rickey walked 2 miles and then another 990 feet. How many miles did Rickey walk in total?
I think the answer is 10,560 feet
Answer:
2.1875 miles
Step-by-step explanation:
1 mile = 5,280 feet
990 feet ÷ 5,280 feet = 0.1875 in miles