Answer:
Step-by-step explanation:
1+tan2A(tanA)=sec2A
Right hand side
sec2A=1cos2A=1cos2A−sin2A
=cos2A+sin2Acos2A−sin2A
=1+tan2A1−tan2A
=1−tan2A+2tan2A1−tan2A
=1−tan2A1−tan2A+2tan2A1−tan2A
=1+2tanA1−tan2A×tanA
=1+tan2A×tanA
=Left hand side
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7x-(5x-1)=2 <------ - - - - - - - - - - - - - - Solve and check the linear equation
Answer:
x= 1/2
Step-by-step explanation:
Solving
7x - (5x - 1) = 27x - 5x + 1 = 22x = 2 -12x = 1x = 1/2Checking
7*1/2 - (5*1/2 - 1) = 27/2 - (5/2 - 1) = 27/2 - 3/2 = 24/2 = 22 = 2The sum of two numbers is four and their product is ten. If one number is x, write an expression for the other number
Answer:
4y - y^2 = 10
Step-by-step explanation:
Let x and y be the two numbers
x+y = 4
xy = 10
Taking the first equation and solving for x
x = 4-y
Substituting this into the second equation
(4-y) *y = 10
4y - y^2 = 10
Lisa built a rectangular flower garden that is 4 meters wide and has a perimeter of 26 meters.
What is the length of Lisa's flower garden?
Given that :-
Width of garden is 4 meters Perimeter of garden is 26 metersTo Find :-
Length of rectangular garden.Solution :-
→ Perimeter = 2( Length + breadth)
→ 26 = 2 ( Length+ 4 )
→ 26/2 = Length + 4
→ 13 = Length + 4
→ Length = 13 -4
→ Length = 9 meters.
So the Length of Lisa's garden is 9 meters .
Answer:
9
Step-by-step explanation:
Represent the following numbers as being members of set K: 2, 4, 2, 0,6, 0, 10, 8
Answer:
Hi, explanation and picture Is below :)
Step-by-step explanation:
K would equal: K = {0, 2, 4, 6, 8, 10}
^^^ (that is in order)^^
That would be the correct expression.
The numbers ‘2 and 0’ are both repeated twice...
So if you want to make it as “members of set” you have to represent each one only once, for it to be members of set...
REVEIW:
Question, Represent the following numbers as being members of set K: 2, 4, 2, 0,6, 0, 10, 8....
Answer, {0, 2, 4, 6, 8, 10}....
By: ✨RobloxYt✨
(Picture attached)
the difference of two number is 28. if one number is 11, find the other number
Answer:
39
Step-by-step explanation:
difference=28
other number=11
so:
11+28=39
39 is your other number
Answer:
Just simply add the given two numbers and you ll get the answer 39 now to check whether its right or wrong subtract 11 from 39 and you ll get 28 which proves that its correct
Step-by-step explanation:
convert 13.025 to base 10
Point M is on line segment \overline{LN} LN . Given LM=5LM=5 and LN=12,LN=12, determine the length \overline{MN}. MN .
Answer: 7 units.
Step-by-step explanation:
Given: Point M is on line segment [tex]\overline{LN}[/tex].
So, point M must divide [tex]\overline{LN}[/tex] into [tex]\overline {LM}[/tex] and [tex]\overline{MN}[/tex].
Such that , [tex]\overline{LN}=\overline{LM}+\overline{MN}[/tex] (i)
Since, [tex]\overline{LM} = 5[/tex] units and [tex]\overline{LN} =12[/tex] units , then we will put values in (i), we will get
[tex]12=5+\overline{MN}\\\\\Rightarrow\overline{MN}=12-5=7[/tex]
Hence, the length of [tex]\overline{MN}[/tex] is 7 units.
What is the relationship between the linear correlation coefficient r and the slope of a regression line?
Answer:
The relationship is that the value of the linear correlation coefficient will always have the same sign as the value of the slope of a regression line.
Step-by-step explanation:
The slope of regression is simply the covariance between X and Y divided by the variance of X i.e Cov(X, Y)/Var X. Whereas, the correlation is the covariance divided by the product of the standard deviation. Thus, we can say that the correlation is the product of the gradient of the regression line and the ratio of the standard deviations.
Thus, it means when the correlation is positive, the slope is also positive and vice versa.
The sign of the correlation coefficient, r, is always the same as that of the slope of the regression line.
Linear Correlation Coefficient and Slope of A Regression LineSlope of a regression line is gotten by dividing the covariance of between X and Y by the variance of X.On the other hand, linear correlation coefficient is gotten by dividing the covariance by the standard deviation.Thus, if the slope of regression line is positive, the correlation coefficient will be positive too and vice versa.Therefore, the sign of the correlation coefficient, r, is always the same as that of the slope of the regression line.
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4z (y+1); use y=3, and z=2
what is the solution of this equation w+8=10
Answer:
the answer is 2
Step-by-step explanation:
you subtract 10 by 8 and get 2, so w would be 2
Answer:
2
Step-by-step explanation:
w+8=10
Subtract 8 on both sides
w+8=10
-8 -8
w=2
Which operations are commutative
and associative
Answer:
addition and multiplication
Step-by-step explanation:
The only operations that can use the commutative and associative properties are addition and multiplication.
Answer:
Step-by-step explanation:
Addition and Multiplication on edg.
An account executive
earns $400 per month
plus a 4% commission
on sales. The executive's
goal is to earn $2800
this month. How much must she sell to achieve this goal?
Answer:
She must sell $60,000
Step-by-step explanation:
4 percent of 60,000 is 2,400 and you add the $400 that she automatically makes every month and you get $2800 as the total amount she makes.
Find the GCF of
66 yx, 30.x²)
Let's first find the greatest common factor of 66 and 30.
To do this, start by dividing 66 by every natural
number you can until you hit repeat factors.
Also note, we need factors that are natural numbers! No decimals!
66 ÷ 1 = 66
66 ÷ 2 = 33
66 ÷ 3 = 22
66 ÷ 6 = 11
We can stop here because if we continue dividing, we hit repeat factors.
So the factors of 66 are 1, 2, 3, 6, 11, 22, 33, and 66.
Now do the same for 30.
30 ÷ 1 = 30
30 ÷ 2 = 15
30 ÷ 3 = 10
30 ÷ 5 = 6
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.
Now look for the largest number shared by the two lists.
In this case, we have 6 as our gcf for the numbers.
Now let's do the variables.
To qualify for the Greatest Common Factor,
the variable must appear in every monomial.
Since the y doesn't appear in every monomial, it does not qualify.
If the variable does appear in every monomial, the Greatest
Common Factor will use the smallest power on that variable.
In this case, the smallest power between x and x² is x.
So our answer is 6x.
Answer:
Mark Me as Brainlieist
Step-by-step explanation:
6x
The time for service call follows a uniform distribution over the interval 20 to 60 minutes.
1. What is the probability that the service call takes longer than 30 minutes?
2. What is the interquartile range?
3. What is the 90th percentile?
Answer:
(1) 0.75
(2) 30
(3) 56
Step-by-step explanation:
Let X represent the time for service call.
It is provided that: [tex]X\sim Uni(20, 60)[/tex]
The probability density function of X is:
[tex]f_{X}(x)=\frac{1}{b-a};\ a<X<b[/tex]
(1)
Compute the probability that the service call takes longer than 30 minutes as follows:
[tex]P(X>30)=\int\limits^{60}_{30} {\frac{1}{60-20}} \, dx[/tex]
[tex]=\frac{1}{40}\times |x|^{60}_{30}\\\\=\frac{60-30}{40}\\\\=\frac{3}{4}\\\\=0.75[/tex]
Thus, the probability that the service call takes longer than 30 minutes is 0.75.
(2)
The Inter quartile range is the difference between the 75th and 25th percentile.
From part (1), we know that P (X > 30) = 0.75.
⇒ 1 - P (X > 30) = 0.75
⇒ P (X < 30) = 0.25
The 25th percentile is 30.
Compute the 75th percentile as follows:
[tex]P(X<x)=0.75\\\\\int\limits^{x}_{20} {\frac{1}{60-20}} \, dx=0.75\\\\\frac{1}{40}\times |x|^{x}_{20}=0.75\\\\x-20=40\times 0.75\\\\x=30+20\\\\x=50[/tex]
The 75th percentile is 50.
Then the inter quartile range is:
[tex]IQR=P_{75}-P_{25}[/tex]
[tex]=50-20\\=30[/tex]
Thus, the inter quartile range is 30.
(3)
Compute the 90th percentile as follows:
[tex]P(X<x)=0.90\\\\\int\limits^{x}_{20} {\frac{1}{60-20}} \, dx=0.90\\\\\frac{1}{40}\times |x|^{x}_{20}=0.90\\\\x-20=40\times 0.90\\\\x=36+20\\\\x=56[/tex]
The 90th percentile is 56.
Larry and Donna bought a sofa at the sale price of $1,536. The original price of the sofa was $1,920.
Answer: $384
Step-by-step explanation:
1000- 1000=0
900-500=400
20-36=-16
400+-16=384
The miles-per-gallon rating of passenger cars is a normally distributed random variable with a mean of 33.8 mpg and a standard deviation of 3.5 mpg. a) What is the probability that a randomly selected passenger car gets more than 37.3 mpg
Answer:
The probability that a randomly selected passenger car gets more than 37.3 mpg is 0.1587.
Step-by-step explanation:
Let the random variable X represent the miles-per-gallon rating of passenger cars.
It is provided that [tex]X\sim N(\mu=33.8,\ \sigma^{2}=3.5^{2})[/tex].
Compute the probability that a randomly selected passenger car gets more than 37.3 mpg as follows:
[tex]P(X>37.3)=P(\frac{X-\mu}{\sigma}>\frac{37.3-33.8}{3.5})[/tex]
[tex]=P(Z>1)\\\\=1-P(Z<1)\\\\=1-0.84134\\\\=0.15866\\\\\approx 0.1587[/tex]
Thus, the probability that a randomly selected passenger car gets more than 37.3 mpg is 0.1587.
Am confused in this y=(2x+1)² –3x
Differentiate y
Answer:
dy/dx = 8x + 1
Step-by-step explanation:
dy/dx = 2(2x+1)*2 - 3
dy/dx = 4(2x + 1) - 3
dy/dx = 8x + 4 - 3
dy/dx = 8x + 1
Solve F(x) for the given domain.
F(x) = x² + 3x - 2
F(3)=____
a. 13
b. 16
C. 40
Answer:
B. 16
Step-by-step explanation:
F(3) means we must plug the number "3" into the equation for each x.
(3)^2 + 3(3) -2
9 + 9 - 2
16
Answer:
16
Step-by-step explanation:
F(x) = x² + 3x - 2
Let x=3
F(3)= 3^2 +3*3 -2
= 9+9-2
= 18-2
=16
1.A bag contains five black and six white balls.
What is the probability of picking a white ball
is it the possible answers
a.1/11
b.6/11
c.1/5
d.5/11
2. 15 road and 25 black balls in a bag.
What is the probability of selecting a black ball from the ball?
is there possible answers
a. 1/25
b.1/5
c.3/8
d.5/8
Answer:
Step-by-step explanation:
no. of black balls = 5
no. of white balls = 6
total no. of balls = 5 + 6 = 11
The probability of picking a white ball = 6/11
no. of red balls = 15
no. of black balls = 25
total no. of balls = 15 + 25 = 40
The probability of selecting a black ball = 25/40
by simplifying,
25/40 = 5/8
hope this helps
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Solve 3(2x+16)=11x+8
What property is illustrated by (2x)y = (2y)x?
Answer:
Commutative property
Step-by-step explanation:
In the Commutative property,the sequence or the order of factors of product does not change the value of the product.
Example:
in
12*5 = 5*12
also 12 = 3*4
(3*4)5 = (3*5)4
_____________________________
given
(2x)y = (2y)x
here it can be written as
(2*x)*y = (2*y)*x
removing the bracket for LHS we have
2*x*y ,
applying Commutative property and changing order of x and y
2*x*y = 2*y*x
now again putting the bracket after first two terms
(2x)y = (2y)x
Thus, the expression illustrates Commutative property.
Orden the Numbers 3/10, 1/5, 0.25 from last yo greatest
Answer:
1/5, 0.25, 3/10
Step-by-step explanation:
1/5=2/10= 0.2
3/10= 0.3
hopefully this is helpful
Answer:
0.25,1/5,3/10 is the order from last to greater.
Step-by-step explanation:
Hope it will help you :)
What’s the perimeter of the square in inches
Answer:
24 inches
Step-by-step explanation:
The perimeter of the shape is 36 inches since the other sides are given as 12 and 3, 6 will be left for the x
12 + 12 + 3 + 3 + x = 36 and x = 6
Susie then drew a square using part of this shape and one side of the square is x inches if one side is x then all fours sides will be x inches
so the perimeter of the square is 4 × x = 24 because we already know x = 6
Use the first and last data points to find the slope intercept equation of a trend line.
Answer:
y = [tex]\frac{16}{3}x-79[/tex]
Step-by-step explanation:
From the given table,
Two points are (1, 15) and (7, 47)
If the two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are lying on a line then slope 'm' of the line will be,
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{47-15}{7-1}[/tex]
= [tex]\frac{32}{6}[/tex]
= [tex]\frac{16}{3}[/tex]
Let the equation of a line passing through (h, k) is,
y - h = m(x - k)
If the line passes through (1, 15)
y - 1 = [tex]\frac{16}{3}(x-15)[/tex]
y = [tex]\frac{16}{3}x-\frac{16}{3}(15)+1[/tex]
y = [tex]\frac{16}{3}x-80+1[/tex]
y = [tex]\frac{16}{3}x-79[/tex]
4 OT
Which of the following are exterior angles? Check all that apply.
4
6
5
3
2
O A. 26
B. 25
C. <3
O D. 24
O E. 22
O F. 21
Answer:
A. <6
Step-by-step explanation:
Exterior angle of this geometric shape is 6
The exterior angle in the given figure is ∠6.
Option A is the correct answer.
What is an angle?The angles between two lines are the angles formed by two intersecting lines, measured in degrees or radians.
Several different types of angles can be formed between two lines, including acute angles, right angles, and obtuse angles.
We have,
From the diagram,
We see that the exterior angle is ∠6.
Now,
The exterior angle is the sum of its two nonadjacent interior angles.
So,
∠6 = ∠1 + ∠3
Thus,
The exterior angle is ∠6.
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plz answer this rnnn plzz will mark a brainliest. it is two pictures.
Answer:
(-1/4, -5 3/4) or (-0.25, -5.75)
Step-by-step explanation:
The hypotheses relating to the discoveries of radium and Neptune may be classified as empirical hypotheses.
a) true
b) false
Answer:
a) true
Step-by-step explanation:
Empirical hypothesis is the type of hypothesis used to try and explain a phenomenon which leads to a theory been developed and put to the test, using observation and experiment.
Radium was discovered due to a discrepancy in pitchblende's radiation. It was noted by the Curies that Polonium alone could not suffice for that amount of radiation, leading to the theory that another element could be present. After further testing, Radium was discovered as the culprit element.
Also, the presence pf another planet, later discovered to be Neptune was theorized to explain the phenomenon that could cause the irregularities in the motion pattern of the planet Uranus. After much experimentation, observations and calculations, Neptune was discovered.
What is the base 10 representation of 11102?
Answer:
14 in base 10.
Step-by-step explanation:
working from right to left we have:
0 + 1*2 + 1*2^2 + 1*2^3
= 0 + 2 + 4 + 8
= 14.
Answer:
14
Step-by-step explanation:
trust me
Verify that the points are the vertices of a parallelogram and find its area. (2,-1,1), (5, 1,4), (0,1,1), (3,3,4)
Answer:
Verified
Area = 13.12 square units.
Step-by-step explanation:
Let the given points / vertices of the parallelogram be represented as follows:
A(2,-1,1),
B(5, 1,4),
C(0,1,1),
D(3,3,4)
In vector notation, we can have;
A = 2i - j + k
B = 5i + j + 4k
C = 0i + j + k
D = 3i + 3j +4k
One of the ways to prove that a quadrilateral is a parallelogram is to show that both pairs of opposite sides are parallel.
(i) Now, let's find the various sides of the assumed parallelogram. These sides are:
AB = B - A = [5i + j + 4k] - [2i - j + k] open the brackets
AB = 5i + j + 4k - 2i + j - k collect like terms and solve
AB = 5i - 2i + j + j - k + 4k
AB = 3i + 2j+ 3k
BC = C - B = [0i + j + k] - [5i + j + 4k] open the brackets
BC = 0i + j + k - 5i - j - 4k collect like terms and solve
BC = 0i - 5i + j - j + k - 4k
BC = -5i + 0j - 3k
CD = D - C = [3i + 3j +4k] - [0i + j + k] open the brackets
CD = 3i + 3j + 4k - 0i - j - k collect like terms and solve
CD = 3i - 0i + 3j - j + 4k - k
CD = 3i + 2j + 3k
DA = A - D = [2i - j + k] - [3i + 3j +4k] open the brackets
DA = 2i - j + k - 3i - 3j - 4k collect like terms and solve
DA = 2i - 3i - j - 3j + k - 4k
DA = - i - 4j - 3k
AC = C - A = [0i + j + k] - [2i - j + k] open the brackets
AC = 0i + j + k - 2i + j - k collect like terms and solve
AC = 0i - 2i + j + j + k - k
AC = - 2i + 2j +0k
BD = D - B = [3i + 3j + 4k] - [5i + j + 4k] open the brackets
BD = 3i + 3j + 4k - 5i - j - 4k collect like terms and solve
BD = 3i - 5i + 3j - j + 4k - 4k
BD = - 2i + 2j + 0k
(ii) From the results in (i) above, it has been shown that;
AB is equal to CD, and that implies that AB is parallel to CD. i.e
AB = CD => AB || CD
Also,
AC is equal to BD, and that implies that AC is parallel to BD. i.e
AC = BD => AC || BD
(iii) Therefore, ABDC is a parallelogram since its opposite sides are equal and parallel.
(B) Now let's calculate the area of the parallelogram.
To calculate the area, we find the magnitude of the cross product between any two adjacent sides.
In this case, we choose sides AC and AB.
Area = | AC x AB |
Where;
[tex]AC X AB = \left[\begin{array}{ccc}i&j&k\\-2&2&0\\3&2&3\end{array}\right][/tex]
AC X AB = i(6 - 0) - j(-6 - 0) + k(-4 -6)
AC X AB = 6i + 6j - 10k
|AC X AB| = [tex]\sqrt{6^2 + 6^2 + (-10)^2} \\[/tex]
|AC X AB| = [tex]\sqrt{36 + 36 + 100} \\[/tex]
|AC X AB| = [tex]\sqrt{172} \\[/tex]
|AC X AB| = 13.12
Therefore the area is 13.12 square units.
PS: The diagram showing this parallelogram has been attached to this response.
A positive integer is twice another.the sum of the reciprocal of the two positive integer is 3/14. Find the integers
Answer:
[tex]\huge\boxed{14\ \text{and}\ 7}[/tex]
Step-by-step explanation:
[tex]n,\ m-\text{positive integer}\\\\n=2m-\text{a positive integer is twice another}\\\\\dfrac{1}{n}+\dfrac{1}{m}=\dfrac{3}{14}-\text{the sum of the reciprocal of the two positive integer is }\ \dfrac{3}{14}\\\\\text{We have the system of equations:}\\\\\left\{\begin{array}{ccc}n=2m&(1)\\\dfrac{1}{n}+\dfrac{1}{m}=\dfrac{3}{14}&(2)\end{array}\right[/tex]
[tex]\text{Substitute (1) to (2):}\\\\\dfrac{1}{2m}+\dfrac{1}{m}=\dfrac{3}{14}\\\\\dfrac{1}{2m}+\dfrac{1\cdot2}{m\cdot2}=\dfrac{3}{14}\\\\\dfrac{1}{2m}+\dfrac{2}{2m}=\dfrac{3}{14}\\\\\dfrac{1+2}{2m}=\dfrac{3}{14}\\\\\dfrac{3}{2m}=\dfrac{3}{14}\Rightarrow2m=14\qquad\text{divide both sides by 2}\\\\\dfrac{2m}{2}=\dfrac{14}{2}\\\\\boxed{m=7}[/tex]
[tex]\text{Substitute it to (1):}\\\\n=2\cdot7\\\\\boxed{n=14}[/tex]