Answer:
A rectangle is a two - dimensional shape, so let me explain using it as an example.
The diagonal of a rectangle divides the rectangle into two triangles that are congruent (the same size and shape.)
Another example is parallelogram; the diagonal of a parallelogram also divides the figure into two separate shapes that are congruent.
Hope this helps!
I really need this answr tonight please HELP!!! Use limits to find the area between the graph of the function and the x axis given by the definite integral. ∫_1^5▒(x^2-x+1)dx
Answer:
[tex]\displaystyle \int\limits^5_1 {(x^2 - x + 1)} \, dx = \frac{100}{3}[/tex]
General Formulas and Concepts:
Calculus
Integration
IntegralsIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \int\limits^5_1 {(x^2 - x + 1)} \, dx[/tex]
Step 2: Integrate
[Integral] Rewrite [Integration Property - Addition/Subtraction]: [tex]\displaystyle \int\limits^5_1 {(x^2 - x + 1)} \, dx = \int\limits^5_1 {x^2} \, dx - \int\limits^5_1 {x} \, dx + \int\limits^5_1 {} \, dx[/tex][Integrals] Integration Rule [Reverse Power Rule]: [tex]\displaystyle \int\limits^5_1 {(x^2 - x + 1)} \, dx = \bigg( \frac{x^3}{3} - \frac{x^2}{2} + x \bigg) \bigg| \limits^5_1[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^5_1 {(x^2 - x + 1)} \, dx = \frac{100}{3}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Answer: 5\int_0^5 3^(3)\sqrt(x^(2)) dx
Step-by-step explanation:
2) Write an equation of a line that would be perpendicular to y = -x-8?
Answer:
Step-by-step explanation:balls
Recent census data indicated that 14.2% of adults between the ages of 25 and 34 live with their parents. A random sample of 125 young adults in this age group was selected. What is the probability that between 14 and 20 of these young adults lived with their parents?
Answer:
The probability is [tex]P(14 < X < 20 ) = 0.5354[/tex]
Step-by-step explanation:
From the question we are told that
The proportion that live with their parents is [tex]\r p = 0.142[/tex]
The sample size is n = 125
Given that there are two possible outcomes and that this outcomes are independent of each other then we can say the Recent census data follows a Binomial distribution
i.e
[tex]X \ \~ \ B( \mu , \sigma )[/tex]
Now the mean is evaluated as
[tex]\mu = n * \r p[/tex]
[tex]\mu = 125 * 0.142[/tex]
[tex]\mu = 17.75[/tex]
Generally the proportion that are not staying with parents is
[tex]\r q = 1 - \r p[/tex]
= > [tex]\r q = 0.858[/tex]
The standard deviation is mathematically evaluated as
[tex]\sigma = \sqrt{n * \r p * \r q }[/tex]
[tex]\sigma = \sqrt{ 125 * 0.142 * 0.858 }[/tex]
[tex]\sigma = 3.90[/tex]
Given the n is large then we can use normal approximation to evaluate the probability as follows
[tex]P(14 < X < 20 ) = P( \frac{ 14 - 17.75}{3.90} <\frac{ X - \mu }{\sigma } < \frac{ 20 - 17.75}{3.90} )[/tex]
Now applying continuity correction
[tex]P(14 < X < 20 ) = P( \frac{ 13.5 - 17.75}{3.90} < \frac{ X - \mu }{\sigma } < \frac{ 19.5 - 17.75}{3.90} )[/tex]
Generally
[tex]\frac{ X - \mu }{\sigma } = Z ( The \ standardized \ value \ of X )[/tex]
[tex]P(14 < X < 20 ) = P( \frac{ 13.5 - 17.75}{3.90} < Z< \frac{ 19.5 - 17.75}{3.90} )[/tex]
[tex]P(14 < X < 20 ) = P( -1.0897 < Z< 0.449 } )[/tex]
[tex]P(14 < X < 20 ) = P( Z< 0.449 ) - P(Z < -1.0897)[/tex]
So for the z - table
[tex]P( Z< 0.449 ) = 0.67328[/tex]
[tex]P(Z < -1.0897) = 0.13792[/tex]
[tex]P(14 < X < 20 ) = 0.67328 - 0.13792[/tex]
[tex]P(14 < X < 20 ) = 0.5354[/tex]
Solve x ^2 + 9x + 8 = 0 by completing the square. What are the solutions?
Answer:
-1 and -8
Step-by-step explanation:
x^2+2*9/2*x+(9/2)^2-(9/2)^2+8=0
(x+9/2)^2+32/4-81/4=0
(x+9/2)^2-49/4=0
(x+9/2)^2=(7/2)^2
so
x+9/2=7/2
x=7/2-9/2
x=-2/2
x=-1
or
x+9/2=-7/2
x=-7/2-9/2=-16/2
x=-8
What is an equation of the line that passes through the point (6, -2) and is parallel
to the line 5x + 3y = 6?
Answer:
y= -5/3x + 8
Step-by-step explanation:
parallel lines have the same slope
5x + 3y = 6
3y = -5x + 6
y = -5/3x + 2
the new line will have the slope (-5/3x)
y = (-5/3x) + b
plug in the (x, y) value to find b
-2 = -5/3(6) + b
-2 = -10 + b
b = 8
your equation is: y= -5/3x + 8
A sales manager for an advertising agency believes that there is a relationship between the number of contacts that a salesperson makes and the amount of sales dollars earned. A regression ANOVA shows the following results: ANOVA df SS MS F Significance F Regression 1.00 13555.42 13555.42 156.38 0.00 Residual 8.00 693.48 86.68 Total 9.00 14248.90 What is the value of the standard error of estimate
Answer:
9.31
Step-by-step explanation:
Given the following :
- - - - - - - - - - df - - - - - SS - - - MS - - - F - - - signiF
Regression - 1 - 13555.42 - 13555.41 - 156.38 - 0
Residual - - 8.00 - 693.48 - - 86.68
Total - - - - 9.00 - 14248.90
What is the value of the standard error of estimate?
The standard error estimate :
Mean square error or Residual (MSE)
Standard Error (SE): √MSE
MSE = 86.68
Standard Error = √86.68
Standard error = 9.3102094
= 9.31
in a school ,there are 150 students .out of these 80 students enrolled for mathematics class, 50 enrolled for English class, and 60 enrolled for physics class . The students enrolled for English cannot attend any other class , but the students of mathematics and physics can take two course at times. find the number of students who have taken both physics and mathematics.
Answer:
40
Step-by-step explanation:
First we need to subtract the 50 students enrolled in English class.
150 - 50 = 100
Next, let's add the mathematics students and the physics students.
80 + 60 = 140
Then we subtract the total amount of mathematics and physics students by the total number of students.
140 - 100 = 40
Therefore, there are 40 students who take both mathematics and physics.
. Which category(s) does 75% belong? I. Real II. Whole III.Rational IV. Integer V. Irrational VI. Natural * A. III and IV only B. I and III only C. I, II, IV, V, and VI only D. I, II, III, IV, and VI only E. I, II, and III
Answer: B.) 1 and 111 only.
Step-by-step explanation:
75% = 75/100 = 0.75
0.75 falls into the category of rational numbers. Rational numbers comprises of numbers which can be expressed in the form a/b where a and b are integers and B is not 0. Here, both 75 and 100 are integers, thus 75% is a rational number.
Irrational numbers are the opposite of rational numbers thus, 75% is not irrational.
All rational numbers and irrational numbers are REAL numbers, hence, 75% is a real number.
Natural numbers are whole digits starting from 1 e.g ( 1, 2, 3,......). Hence 75% is not a natural number
Whole numbers are natural numbers including 0. (0, 1, 2,.....). Hence, 75% is not a whole number
Integer numbers are comprises of both positive and negative whole numbers. (..., - 1, - 2, 0, 1, 2,...). Hence, 75% is not an integer.
For 15 points!!!
If vectors i+j+2k, i+pj+5k and 5i+3j+4k are linearly dependent, the value of p is what?
Please I'm looking for the explanation. i already know the answer is 2, i just don't know how.
Answer:
(D) 2
Step-by-step explanation:
If two or more vectors are linearly dependent, then one of them can be expressed as a linear combination of the rest. In other words, vectors are dependent linearly on one another if the determinant of the matrix that they form is zero.
Given vectors:
i+j+2k
i+pj+5k
5i+3j+4k
Now, since they are linearly dependent, then the determinant of their matrix should be zero. i.e
Let their matrix be A and is given by;
A = [tex]\left[\begin{array}{ccc}1&1&2\\1&p&5\\5&3&4\end{array}\right][/tex]
Where;
the first column holds the i components of the vectors
the second column holds the j components of the vectors and
the third column holds the k components of the vectors
=> |A| = det(A) = 0
[tex]det(A) = det \left[\begin{array}{ccc}1&1&2\\1&p&5\\5&3&4\end{array}\right] = 0[/tex]
Now, let's calculate the determinant.
[tex]det \left[\begin{array}{ccc}1&1&2\\1&p&5\\5&3&4\end{array}\right] = 1(4p - 15) - 1(4 - 25) + 2(3 - 5p) = 0[/tex]
=> 4p -15 - 4 + 25 + 6 - 10p = 0
=> 4p - 10p + 12 = 0
=> 6p = 12
=> p = 2
Therefore, the value of p for which the vectors are linearly dependent is 2
A school P is 16km due west of a school Q. what is the bearing of Q from P
Answer:
16Km due east of school P
Step-by-step explanation:
Given
A school P is 16km due west of a school Q
Thus, we can say that distance PQ = 16 km.
________________________________
now we have to find the bearing of Q from P
As distance is same
distance PQ = distance QP
Thus,
Distance will remain same of 16 km.
For direction,
If Q is west of P, then P will be east of Q[tex]P------------------>Q[/tex]
as shown in figure P is west of Q,
now from point P , Q is west P.
Thus,
Bearing of School Q from P is 16Km due east of school P
Simplify 1 - 3s - s + 8 - 2
Step-by-step explanation:
first you group like terms.
-3s-s+8+1-2
-4s+7
Answer:
-4s + 7
Step-by-step explanation:
We need to combine like terms. Like terms are terms whose variables (and exponents) are the same (note that they could be constants as well). Basically, they are "like" each other. In this case, the like terms are -3s and - s and also 1, 8, and -2. -3s - s = -4s and 1 + 8 - 2 = 7 so the answer is -4s + 7.
The data show systolic and diastolic blood pressure of certain people. Find the regression equation, letting the systolic reading be the independent (x) variable. Find the best predicted diastolic pressure for a person with a systolic reading of 146 . Is the predicted value close to 91.0 , which was the actual diastolicreading? Use a significance level of 0.05.Systolic 117 134 150 113 138 113 144 145Diastolic 85 74 86 55 75 80 106 841. What is the regression equation? (Round to two decimal places as needed.)2. What is the best predicted diastolic pressure for a person with a systolic reading of 146 ?3. Is the predicted value close to 91.0 , which was the actual diastolic reading?A. The predicted value is very close to the actual diastolic reading.B. The predicted value is not close to the actual diastolic reading.C. The predicted value is close to the actual diastolic reading.D. The predicted value is exactly the same as the actual diastolic reading.
Answer:
ŷ = 6.69X - 706.18 ; ŷ = 270.56 ; B. The predicted value is not close to the actual diastolic reading.
Step-by-step explanation:
Systolic reading(x) :
117
134
150
113
138
113
144
145
Diastolic (y) :
85
74
86
55
75
80
106
841
Using the online regression calculator, the regression equation obtained using the data values provided above is:
ŷ = 6.69X - 706.18
Comparing with the regression equation formula: ŷ = mX + c
Where :
ŷ = predicted variable (Diastolic)
m = 6.69 = gradient or slope of the regression line
c = - 706.18 = intercept ( where the regression line intersects the y-axis).
2.) What is the best predicted diastolic pressure for a person with a systolic reading of 146
X = 146
ŷ = 6.69(146) - 706.18
ŷ = 976.74 - 706.18
ŷ = 270.56
The predicted value, 270.56 is not close to the actual Diastolic reading of 91.0
55 POINTS Camille and Hiroshi are trying to determine the most number of lines that can be drawn using any two of four random points. Is either correct? Explain.
please explain i want to understand it
Hiroshi is correct; after you draw
the line from the first point to the other three, one of
the lines from the second point is already drawn.
subtract the sum of -1 37 and - 43 from the sum of - 103 and 27
Step-by-step explanation:
Hey, there!!
I hope you mean to subtract (-137) +(-43) from sum of -103 and 27.
First, add -103 + 27
[tex] = - 103 + 27[/tex]
[tex] = - 76[/tex]
{As ( minus + plus )= subtracts with sign which has greator value. }
now,
[tex]( - 137) + ( - 43) = - 180[/tex]
{ minus + minus = add with minus sign}.
Now, subtracting -180 from -76.
=(-76) - (-180 )
Now, multiply the sign (- × -)= +
so, -180 becomes +180
= -76+180
= 104..... is answer.
Hope it helps...
Answer:
104
Step-by-step explanation:
With what you provide, the expression would be:
[tex](-103+27)-(-137+-43)[/tex], which equals to:
[tex](-76)-(-180)= (-76)+(180)=104[/tex]. [negative minus a negative equals positive]
So, the answer would be 104.
Cicero and Themistocles run for the same political office.
Cicero received w votes in the election, and Themistocles
received v votes.
Which of the following expressions always represents
how many more votes the winner received than the
loser?
Choose 1 answer:
W-V
|w - u
None of the above
Answer:
|w - v| or |v - w|
Step-by-step explanation:
The answer is the absolute value of the difference of the two numbers written in either order.
|w - v| or |v - w|
Answer:
B |w-v|
Step-by-step explanation:
khan academy
a triangular flag has an area of 0.75 square feet and height of 1.5 foot. what is the base
Answer:
1 foot
Step-by-step explanation:
Using the formula for the area of a triangle, fill in the given information and solve for the unknown.
A = (1/2)bh
0.75 = (1/2)b(1.5)
b = 0.75/0.75 = 1 . . . . divide by the coefficient of b
The base is 1 foot.
Please help! I’ll mark you as brainliest if correct
Answer:
3. C
Step-by-step explanation:
16 / 4 = 4 which is a counting number.
- 30 / 5 = -6 which is a integer.
-31/8 = -3.875 which is rational number
30/9 = 10/3 = 3.333333333.... which is an irrational number
So your answer is C
A pancake recipe calls for 1 cup of flour. Derek has already used 1/4 cup of flour. How many more cups of flour does Derek need to add?
Answer:
Derek needs to add 3/4 cups of flour.
Step-by-step explanation:
If Derek has already used 1/4 cup of flour, he needs 3 more cups of flour to get to 1 full cup of flour.
Answer:
Step-by-step explanation:A batch of cookies requires 2 1/4 cup of flour and 1 egg. You have in your kitchen 8 cups of flour and a half dozen eggs. a) How many batches of cookies
Find the vector projection of B onto A if A = 5i + 11j – 2k,B = 4i + 7k
Answer:
[tex]\frac{3}{13} i+\frac{11}{130} j-\frac{6}{65} k\\[/tex]
Step-by-step explanation:
Given A = 5i + 11j – 2k and B = 4i + 7k, the vector projection of B unto a is expressed as [tex]proj_ab = \dfrac{b.a}{||a||^2} * a[/tex]
b.a = (5i + 11j – 2k)*( 4i + 0j + 7k)
note that i.i = j.j = k.k =1
b.a = 5(4)+11(0)-2(7)
b.a = 20-14
b.a = 6
||a|| = √5²+11²+(-2)²
||a|| = √25+121+4
||a|| = √130
square both sides
||a||² = (√130)
||a||² = 130
[tex]proj_ab = \dfrac{6}{130} * (5i+11j-2k)\\\\proj_ab = \frac{30}{130} i+\frac{11}{130} j-\frac{12}{130} k\\\\proj_ab = \frac{3}{13} i+\frac{11}{130} j-\frac{6}{65} k\\\\[/tex]
Hence the projection of b unto a is expressed as [tex]\frac{3}{13} i+\frac{11}{130} j-\frac{6}{65} k\\[/tex]
Please help me, I don't understand how to do this! :(
Answer:
1/273
Step-by-step explanation:
5/15 * 4/14 * 3/13 * 2/12
= 1/3 * 2/7 * 3/13 * 1/6
= 1/273
You travel from City X to City Y. You know that the round-trip distance is 647 miles. City Z, a city you pass on the way, is 27 miles from City X. Find the distance from City Z to City Y. The distance from City Z to City Y is miles.
Answer:
296.5 miles
Step-by-step explanation:
Round trip distance of City X to City Y is 647 miles.
Round trip includes to and fro.
i.e. City X to City Y and then City Y to City X back.
Let the distance between City X and City Y = D
Distance traveled in round trip between City X and City Y = D + D = 2D
Given than 2D = 647
OR
D = [tex]\frac{647}2[/tex] = 323.5 miles
Kindly refer to the attached diagram, for the location of City Z.
Distance between XY = Distance from X to Z + Distance from Z to Y.
Distance XY = XZ +ZY
323.5 = 27 +ZY
ZY =296.5 miles
What value goes in box A?
What value goes in box B?
What value goes in box C?
What value goes in box D?
URGENT HURRYY PLEASE
Step-by-step explanation:
Hello!
For this you multiply the numbers that intersect at that box
Box A 2x and 4 intersect
2x * 4 = 8x
Box B 3 and 4 intersect
3 * 4 = 12
Box C 2x and x intersect
2x * x = [tex]2x^{2}[/tex]
Box D 3 and x intersect
3 * x = 3x
To solve this we put all these together
[tex]2x^{2} +3x+8x+12[/tex]
Combine like terms
[tex]2x^{2} +11x+12[/tex]
Hope this helps!
Find the sum of all $r$ such that $\frac{8r^2 - 14 r + 3}{r+5} = 4r -1$.
Answer:
8.25
Step-by-step explanation:
[tex]\frac{8r^2 - 14 r + 3}{r+5} = 4r -1[/tex]
[tex]8r^2 - 14r + 3= (4r -1)(r + 5)[/tex]
[tex]8r^2 - 14r + 3= 4 {r}^{2} + 19r - 5[/tex]
[tex]4 {r}^{2} - 33r + 8=0[/tex]
[tex]4 {r}^{2} - 32r - r + 8 = 0[/tex]
[tex]4r(r - 8) - 1(r - 8) = 0[/tex]
[tex](4r - 1)(r - 8)[/tex]
[tex]r = 8 \: or \: \frac{1}{4} [/tex]
Therefore the sum of all values of r
[tex]8 + \frac{1}{4} = 8 \frac{1}{4} [/tex]
Please help me please
Answer:
B
Step-by-step explanation:
So we have a 45-45-90 triangle.
This is a special right triangle. In a 45-45-90 triangle, the side lengths are x, and the hypotenuse will be x√2
Since the hypotenuse is 3, we can set it equal to x√2 to solve for x. Therefore:
[tex]x\sqrt2=3[/tex]
Divide both sides by √2:
[tex]x=\frac{3}{\sqrt2}[/tex]
Rationalize:
[tex]x=\frac{3\sqrt2}{2}[/tex]
Our answer is B.
find the x-intercept for y=x^2+4x+5
Answer: There is no x-intercept for this quadratic equation.
Step-by-step explanation:
An x-intercept is when the y-value of the point if equal to zero. There is no x-intercept for this quadratic equation. This can be supported by the fact that this equation cannot be factored.
Given the equation p = 2n – 3, what is p when=3
Answer:
n = 3
Step-by-step explanation:
Hello!
p = 2n - 3
the question asks for when p is equal to 3 so we put 3 in for p
3 = 2n - 3
Now we can solve this
3 = 2n - 3
Add 3 to both sides
6 = 2n
Divide both sides by 2
3 = n
The answer is n = 3
Hope this Helps!
Find the equation that best represents the following word problem: In a certain freshman class, the number of girls is 83 less than twice the number of boys (b). The total number of students in that freshman class is 259. How many boys and girls are in that class? A) b + 2b = 259 - 83 B) b + 2b – 83 = 259 C) b + 83 – 2b = 259 D) b + 2b = 259
Answer:
(B) [tex]b + 2b - 83 = 259[/tex]
Step-by-step explanation:
We can first create the equation [tex]b + g = 259[/tex], since we know that there are a total of 259 students in this freshman class.
Now, the amount of girls is 83 less than twice the number of boys, so that is [tex]2b - 83[/tex].
Now, we can substitute this in the previous equation as g.
[tex]b + 2b - 83 = 259[/tex]
Hope this helped!
Answer:
b
Step-by-step explanation:
Veronica wants to check her work after evaluating . What steps can she follow to verify her answer?
Divide her answer by –6 and see if the result is –108.
Divide her answer by –108 and see if the result is –6.
Multiply her answer by –6 and see if the result is –108.
Multiply her answer by –108 and see if the result is –6.
Answer:The answer is C
Step-by-step explanation:
I just had the question and i got it right :D
Declan says that for any number n the product 4 x n is greater than 4 which vaule of n shows why Declan incorrect
Answer:
see below (I hope this helps!)
Step-by-step explanation:
When n < 1, Declan's statement is incorrect because 4 * 0 = 0 which is not greater than 4 and this continues for all n values that are less than 1.
Please help me
Write an equation for the question
You withdraw $100 from the ATM machine. The new balance is $372. What was the ordinary balance b of your account?
Answer:
B-$100=$372
The is is the smartest way I could look at this
OR
$372 - $100= b
Hope this helps
MARNIE OUT!