Step-by-step explanation:
( secA + 1)( sec A - 1)
Using the expansion
( a + b)( a - b) = a² - b²
Expand the expression
We have
sec²A + secA - secA - 1
That's
sec² A - 1
From trigonometric identities
sec²A - 1 = tan ²ASo we have the final answer as
tan²AAs proven
Hope this helps you
Step-by-step explanation:
Here,
LHS
= (SecA+1)(secA -1)
[tex] = {sec}^{2} A - 1[/tex]
[tex]{as{a}^{2} - {b}^{2} =(a + b)(a - b)[/tex]
Now, we have formula that:
[tex] {sec}^{2} \alpha - {tan \alpha }^{2} = 1[/tex]
[tex] {tan}^{2} \alpha = {sec }^{2} \alpha - 1[/tex]
as we got ,
[tex] = {sec}^{2} A- 1[/tex]
This is equal to:
[tex] = {tan}^{2} A[/tex]
= RHS proved.
Hope it helps....
An ESP experiment used the "Ten Choice Trainer." This is like the Aquarius, but with 10 targets instead of 4. Suppose that in 1,000 trials, a subject scores 173 correct guesses.
Required:
a. Set up the null hypothesis as a box model.
b. The SD of the box is:_______
c. Make the z-test.
d. What do you conclude?
Answer:
a. The H0 is number of correct guesses is 173
b. Standard Deviation of box is 0.3
c. z-test value is 7.70
d. The difference does not appear due to chances of Variation.
Step-by-step explanation:
The standard deviation is :
[tex]\sqrt{0.1 * 0.9}[/tex] = 0.3
The standard deviation of the box is 0.3 approximately.
Z-score is [tex]\frac{x-u}{standard error}[/tex]
Z-score = [tex]\frac{173-100}{9.4868}[/tex]
the value of z-score is 7.70.
3. a) Why is X3 is a polynomial but
[tex] \frac{7}{x {}^{2} } [/tex]
, is not a polynomial? write in your words.
Answer:
because the power of variable is -2
Step-by-step explanation:
polynomials are a combination of constant and variable or only variable, being that power of variable is always positive natural no.
7/x^2 denotes 7x^-2
answer no explantion pls i need asap
Answer:
Below.
Step-by-step explanation:
Area = 5(x + 3)
= 5x + 15
Perimeter = 2(x + 3) + 2(5)
= 2x + 6 + 10
= 2x + 16.
Customers receive rewards pints based on the purchase type:
log 7 (x^2 + 11) = log 7 15
Answer:
x = ±2
Step-by-step explanation:
log 7 (x^2 + 11) = log 7 15
We know that log a ( b) = log a(c) means b =c
x^2 + 11 = 15
Subtract 11 from each side
x^2 = 15-11
x^2 =4
Take the square root of each side
sqrt(x^2) =±sqrt(4)
x = ±2
What is the value of log,1252
PERE
3
5
Ο ΟΟΟ
15
Mark this and return
Save and Exit
Next
Can someone please help me ASAP:(
Answer:
3 =x
Step-by-step explanation:
(segment piece) x (segment piece) = (segment piece) x (segment piece)
3x(x+1) = 4x*x
Divide each side by x
3(x+1) = 4x
Distribute
3x+3 = 4x
Subtract 3x from each side
3x-3x +3 = 4x-3x
3 =x
Billy has x marbles. Write an
expression for the number of
marbles the following have…
a) Charlie has 5 more than Billy
b) Danny has 8 fewer than Billy
c) Eric has three times as many as
Billy
Answer:
[tex]Charlie = 5 + x[/tex]
[tex]Danny = x - 8[/tex]
[tex]Eric = 3x[/tex]
Step-by-step explanation:
Given
Billy's Marble = x
Required
Determine a,b and c
a. Charlie's Marble
"5 more" means 5 + or + 5
Since Billy's Marble is represented with x, then Charlie's Marbles will be
[tex]Charlie = 5 + x[/tex]
b. Danny's Marbles
Having "8 fewer" means we have to subtract 8 from Billy's marble;
Since Billy's Marble is represented with x, then Danny's Marbles will be
[tex]Danny = x - 8[/tex]
c. Eric Marbles
Having "three times as " means we have to multiply Bill's marble by 3;
Since Billy's Marble is represented with x, then Danny's Marbles will be
[tex]Eric = 3 * x[/tex]
[tex]Eric = 3x[/tex]
An expression is ???
Answer:
s-6
Step-by-step explanation:
difference means subtract
s-6
the x coordinates of the point where 2y-x=10 intersect the line y=3x
Answer:
5
Step-by-step explanation:
2y=10+x
y=3x
Equalizing both sides:
10+x=3x
10=3x-x
10=2x
x=5
Sophia runs twice as fast as her friend Mia. If mia runs 3 mph how long will it tske sophia to run 6 miles? 9 miles?
Answer:
It will take Sophia 1 hour to run 6 miles.
And 1 1/2 hours for 9 miles.
Step-by-step explanation:
Let E and F be two events of an experiment with sample space S. Suppose P(E) = 0.6, P(F) = 0.3, and P(E ∩ F) = 0.1. Compute the values below.
(a) P(E ∪ F) =
(b) P(Ec) =
(c) P(Fc ) =
(d) P(Ec ∩ F) =
Answer:
(a) P(E∪F)= 0.8
(b) P(Ec)= 0.4
(c) P(Fc)= 0.7
(d) P(Ec∩F)= 0.8
Step-by-step explanation:
(a) It is called a union of two events A and B, and A ∪ B (read as "A union B") is designated to the event formed by all the elements of A and all of B. The event A∪B occurs when they do A or B or both.
If the events are not mutually exclusive, the union of A and B is the sum of the probabilities of the events together, from which the probability of the intersection of the events will be subtracted:
P(A∪B) = P(A) + P(B) - P(A∩B)
In this case:
P(E∪F)= P(E) + P(F) - P(E∩F)
Being P(E) = 0.6, P(F) = 0.3 and P(E ∩ F) = 0.1
P(E∪F)= 0.6 + 0.3 - 0.1
P(E∪F)= 0.8
(b) The complement of an event A is defined as the set that contains all the elements of the sample space that do not belong to A. The Complementary Rule establishes that the sum of the probabilities of an event and its complement must be equal to 1. So, if P (A) is the probability that an event A occurs, then the probability that A does NOT occur is P (Ac) = 1- P (A)
In this case: P(Ec)= 1 - P(E)
Then: P(Ec)= 1 - 0.6
P(Ec)= 0.4
(c) In this case: P(Fc)= 1 - P(F)
Then: P(Fc)= 1 - 0.3
P(Fc)= 0.7
(d) The intersection of two events A and B, designated as A ∩ B (read as "A intersection B") is the event formed by the elements that belong simultaneously to A and B. The event A ∩ B occurs when A and B do at once.
As mentioned, the complementary rule states that the sum of the probabilities of an event and its complement must equal 1. Then:
P(Ec intersection F) + P(E intersection F) = P(F)
P(Ec intersection F) + 0.1 = 0.3
P(Ec intersection F)= 0.2
Being:
P(Ec∪F)= P(Ec) + P(F) - P(Ec∩F)
you get:
P(Ec∩F)= P(Ec) + P(F) - P(Ec∪F)
So:
P(Ec∩F)= 0.4 + 0.3 - 0.2
P(Ec∩F)= 0.8
If the average yield of cucumber acre is 800 kg, with a variance 1600 kg, and that the amount of the cucumber follows the normal distribution. 1- What percentage of a cucumber give the crop amount between 778 and 834 kg? 2- What the probability of cucumber give the crop exceed 900 kg ?
Answer:
a
The percentage is
[tex]P(x_1 < X < x_2 ) = 51.1 \%[/tex]
b
The probability is [tex]P(Z > 2.5 ) = 0.0062097[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 800[/tex]
The variance is [tex]var(x) = 1600 \ kg[/tex]
The range consider is [tex]x_1 = 778 \ kg \ x_2 = 834 \ kg[/tex]
The value consider in second question is [tex]x = 900 \ kg[/tex]
Generally the standard deviation is mathematically represented as
[tex]\sigma = \sqrt{var (x)}[/tex]
substituting value
[tex]\sigma = \sqrt{1600}[/tex]
[tex]\sigma = 40[/tex]
The percentage of a cucumber give the crop amount between 778 and 834 kg is mathematically represented as
[tex]P(x_1 < X < x_2 ) = P( \frac{x_1 - \mu }{\sigma} < \frac{X - \mu }{ \sigma } < \frac{x_2 - \mu }{\sigma } )[/tex]
Generally [tex]\frac{X - \mu }{ \sigma } = Z (standardized \ value \ of \ X)[/tex]
So
[tex]P(x_1 < X < x_2 ) = P( \frac{778 - 800 }{40} < Z< \frac{834 - 800 }{40 } )[/tex]
[tex]P(x_1 < X < x_2 ) = P(z_2 < 0.85) - P(z_1 < -0.55)[/tex]
From the z-table the value for [tex]P(z_1 < 0.85) = 0.80234[/tex]
and [tex]P(z_1 < -0.55) = 0.29116[/tex]
So
[tex]P(x_1 < X < x_2 ) = 0.80234 - 0.29116[/tex]
[tex]P(x_1 < X < x_2 ) = 0.51118[/tex]
The percentage is
[tex]P(x_1 < X < x_2 ) = 51.1 \%[/tex]
The probability of cucumber give the crop exceed 900 kg is mathematically represented as
[tex]P(X > x ) = P(\frac{X - \mu }{\sigma } > \frac{x - \mu }{\sigma } )[/tex]
substituting values
[tex]P(X > x ) = P( \frac{X - \mu }{\sigma } >\frac{900 - 800 }{40 } )[/tex]
[tex]P(X > x ) = P(Z >2.5 )[/tex]
From the z-table the value for [tex]P(Z > 2.5 ) = 0.0062097[/tex]
Nina skated for 2 hours and 14 min she stop at 8:24 pm when did Nina start skating
Answer:
6:10
Step-by-step explanation:
if z and (z+50) are supplement of each other find the value of z
Answer:
z=65
Step-by-step explanation:
supplementary angles means sum of those angles is 180 degrees
so,
z+z+50=180
2z=130
z=65
I did the best I could, I'm 12 don't judge me.
The size of a television is the length of the diagonal of its screen in inches. The aspect ratio of the screens of older televisions is 4:3, while the aspect ratio of newer wide-screen televisions is 16:9. Find the width and height of an older 35-inch television whose screen has an aspect ratio of 4:3.
Answer:
The Width = 28 inches
The Height = 21 inches
Step-by-step explanation:
We are told in the question that:
The width and height of an older 35-inch television whose screen has an aspect ratio of 4:3
Using Pythagoras Theorem
Width² + Height² = Diagonal²
Since we known that the size of a television is the length of the diagonal of its screen in inches.
Hence, for this new TV
Width² + Height² = 35²
We are given ratio: 4:3 as aspect ratio
Width = 4x
Height = 3x
(4x)² +(3x)² = 35²
= 16x² + 9x² = 35²
25x² = 1225
x² = 1225/25
x² = 49
x = √49
x = 7
Hence, for the 35 inch tv set
The Width = 4x
= 4 × 7
= 28 inches.
The Height = 3x
= 3 × 7
= 21 inches
Can someone help me by solving this?
Answer:
30000 times 2.28 equals 68 400
Step-by-step explanation:
prove (sinxsiny-cosxcosy)(sinxsiny+cosxcosy) =sin^2x-cos^2y
Step-by-step explanation:
Recall that [tex]\sin^2x + \cos^2x = 1[/tex]
[tex](\sin x \sin y - \cos x \cos y)(\sin x \sin y + \cos x \cos y)[/tex]
[tex]= \sin^2 x \sin^2 y - \cos^2 x \cos^2 y[/tex]
[tex]= \sin^2 x (1 - \cos^2 y) - \cos^2 x \cos^2 y[/tex]
[tex]= \sin^2 x - \sin^2 x \cos^2y - \cos^2x \cos^2y[/tex]
[tex]= \sin^2x - (\sin^2x + \cos^2x)\cos^2y[/tex]
[tex]= \sin^2x - \cos^2y[/tex]
The difference between two positive integers is 7 and the sum of their squares is 949. What are the numbers?
Answer:
25 and 18
Step-by-step explanation:
Let's say that the first number is x and the second one is y.
First, the difference between them is 7, so x-y=7
Next, the sum of their squares is 949, so x²+y² = 949
We have
x-y=7
x²+y²=949
One thing we can do to solve this problem is to solve for x in the first equation, plug that into the second equation, and go from there
Adding y to both sides in the first equation, we have
x = 7 + y
Plugging that into the second equation for x, we have
(7+y)²+ y² = 949
expand
(7+y)(7+y) + y² = 949
49 + y² + 7y + 7y + y² = 949
combine like terms
2y² +14y + 49 = 949
subtract 949 from both sides to put this in the form of a quadratic equation
2y² + 14y - 900 = 0
divide both sides by 2
y² + 7y - 450 = 0
To factor this, we want to find 2 numbers that add up to 7 and multiply to -450.
The factors of 450 are as follows:
1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, and 450.
Note that we want to find two numbers with a difference of 7, as one will have to be negative for the multiplication to end up at -450. Two numbers that stand out are 18 and 25. To make them add up to 7, 18 can be negative. We therefore have
y² + 25y - 18y - 450 = 0
y(y+25) - 18(y+25) = 0
(y-18)(y+25) = 0
Solving for 0,
y-18 = 0
add 18 to both sides
y=18
y+25 = 0
subtract 25 from both sides
y= -25
As the question states "two positive integers", this means that y must be positive, so y = 18. We know x-y=7, so
x-18 = 7
add 18 to both sides to isolate x
x = 25
what is the domain of f(x)=(1/4)^x
Answer:
B All real numbers
hope you wil understand
Answer:
[tex]\boxed{\sf B. \ All \ real \ numbers}[/tex]
Step-by-step explanation:
The domain is all possible values for x.
[tex]f(x)=(\frac{1}{4} )^x[/tex]
There are no restrictions on the value of x.
The domain is all real numbers.
Carol owns a BBQ company that sells brisket for $11.75 per pound (after it is smoked for 10 hours). She buys the brisket for an AP$ of $4.72 per pound and they weigh 10.4 lbs each. Once they are done smoking, they weigh 6.24 lbs each.
What is the yield % of the briskets after Carol is done smoking them?
Answer: 60%
Step-by-step explanation:
Given, AP$ of Brisket = $4.72
Weight of each brisket on purchase : 10.4 lbs
Weight of each brisket after smoking : 6.24 lbs
Yield % of the briskets after Carol is done smoking them=[tex]\dfrac{\text{Weight after smoking}}{\text{Weight on purchase}}[/tex]
[tex]\dfrac{6.24}{10.4}\times100\\\\=60\%[/tex]
Hence, the yield % of the briskets after Carol is done smoking them = 60%
To find ∫ (x − y) dx + (x + y) dy directly, we must parameterize C. Since C is a circle with radius 2 centered at the origin, then a parameterization is the following. (Use t as the independent variable.)
x = 2 cos(t)
y = 2 sin(t)
0 ≤ t ≤ 2π
With this parameterization, find the followings
dy=_____
dx=_____
Answer:
Step-by-step explanation:
Hello, please consider the following.
[tex]x=x(t)=2cos(t)\\\\dx=\dfrac{dx}{dt}dt=x'(t)dt=-2sin(t)dt[/tex]
and
[tex]y=y(t)=2sin(t)\\\\dy=\dfrac{dy}{dt}dt=y'(t)dt=2cos(t)dt[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
The values of dx and dy are give as -2sin(t)dt and 2cos(t)dt respectively. The answer to the given problem can be stated as,
dy = 2cos(t)dt
And, dx = -2sin(t)dt.
What is the integration of a function?The integration can be defined as the inverse operation of differentiation. If a function is the integration of some function f(x) , then differentiation of that function is f(x).
The given integral over C is ∫ (x − y) dx + (x + y) dy.
And, the parameters for C are as follows,
x = 2cos(t)
y = 2sin(t)
0 ≤ t ≤ 2π
Now, on the basis of these parameters dx and dy can be found as follows,
x = 2cos(t)
Differentiate both sides with respect to t as follows,
dx/dt = 2d(cos(t))/dt
=> dx/dt = -2sin(t)
=> dx = -2sin(t)dt
And, y = 2sin(t)
Differentiate both sides with respect to t as follows,
dy/dt = 2d(sin(t))/dt
=> dy/dt = 2cos(t)
=> dy = 2cos(t)dt
Hence, the value of dx and dy as per the given parameters is -2sin(t)dt and 2cos(t)dt respectively.
To know more about integration click on,
https://brainly.com/question/18125359
#SPJ2
The sum of the first 5 terms of an AP is 30 and the sum of the four term from T6 to T9 (inclusive) is 69. Find the AP
Answer: The AP = 1, ⁷/₂, 6, ¹⁷/₂, 11 ..............
Step-by-step explanation:
From the first statement,
S₅ = ⁵/₂(2a + ( n - 1 )d } = 30
5(2a + 4d )d = 60
10a + 20d = 60
reduce to lowest term to easy calculation by dividing through by 10
a + 2d = 6 -----------------------------------1
second statement
sum of the next 4 terms inclusive
T₉ = ⁹/₂(2a + 8d ) = 69
9(2a + 8d ) = 30 + 69
18a + 72d = 99 x 2
18a + 72d = 198
divide through by 18 to reduce to lowest time
a + 4d = 11 ------------------------------------------2
Now solve the two equation simultaneously to find a and d
a + 2d = 6
a + 4d = 11
-2d = -5
d = ⁵/₂.
Now substitute for d to get a
a + 2(⁵/₂) = 6
a + 5 = 6
a = 6 - 5
a = 1.
Therefore the AP = 1 , ⁷/₂ , 6 , ¹⁷/₂ , 11 , ..............
The AP if, The sum of the first 5 terms of an AP is 30 and the sum of the four terms from T6 to T9 is 69, is 1, ⁷/₂, 6, ¹⁷/₂, 11, and so on.
What is sequence?
An ordered collection of objects that allows repetitions is referred to as a sequence. It has members, just like a set does. The length of the sequence is determined by the number of items.
Given:
The sum of the first 5 terms of an AP is 30,
Write the equations as shown below,
S₅ = ⁵/₂(2a + ( n - 1 )d } = 30
5(2a + 4d )d = 60
10a + 20d = 60
reduce to lowest term to easy calculation by dividing through by 10
a + 2d = 6
T₉ = ⁹/₂(2a + 8d ) = 69 (sum of the next 4 terms inclusive)
9(2a + 8d ) = 30 + 69
18a + 72d = 99 x 2
18a + 72d = 198
a + 4d = 11
Solve the equation as shown below,
d = ⁵/₂, and a = 1.
Therefore, the AP = 1, ⁷/₂, 6, ¹⁷/₂, 11, and so on.
To know more about the sequence:
https://brainly.com/question/28615767
#SPJ5
I ONLY need 8c
Please show ALL STEPS
Answer:
8c
f(g(x)) = x^4 + 2x^3 - x
g(f(x)) = x^4 + 2x^3 + 2x^2 - x
Step-by-step explanation:
f(x) = x^2 - x ; g(x) = x^2 + x
f(g(x)) = (x^2 + x)^2 - (x^2 + x)
f(g(x)) = (x^2 + x)^2 - x^2 - x
f(g(x)) = (x^2 + x)(x^2 + x) - x^2 - x
f(g(x)) = x^4 + x^3 + x^3 + x^2 - x^2 - x
f(g(x)) = x^4 + 2x^3 - x
g(f(x)) = (x^2 - x)^2 + x^2 - x
g(f(x)) = (x^2 + x)(x^2 + x) + x^2 - x
g(f(x)) = x^4 + x^3 + x^3 + x^2 + x^2 - x
g(f(x)) = x^4 + 2x^3 + 2x^2 - x
boat costs $54,000. you pay 10% down and amortize the rest with equal monthly payments over a 15 year period. If you must pay 4.5 % comounded monthly, what is your monthly payment?
3385.8
Step-by-step explanation:
If a teacher's guide to a popular SAT workbook is to be printed using a special type of paper, the guide must have at most 400 pages. If the publishing company charges 1 cent per page printed, what is the largest price, in dollars, that can be charged to print 20 copies of the workbook using the special paper?
Answer:
$80
Step-by-step explanation:
To find the largest price, assume that all 20 copies of the workbook will have 400 pages.
Since the company charges 1 cent per page, this means each workbook will cost 400 cents. This is equivalent to 4 dollars.
Find the total cost by multiplying this by 20:
20(4)
= 80
So, the largest price to print 20 copies is $80
let f(x) = 9x - 2 and g(x) = -x + 3. find f(g(x)). a. -9x - 2 b. -9x + 5 c. -9x + 25 d. -9x + 27
Answer:
See below.
Step-by-step explanation:
[tex]f(x)=9x-2 \text{ and } g(x)=-x+3\\f(g(x))=f(-x+3)\\f(-x+3)=9(-x+3)-2\\\text{Distribute and Simplify}\\-9x+27-2\\=-9x+25\\\text{Therefore, f(g(x))=-9x+25}\\\text{The answer is C}[/tex]
find the measure of x
Answer:
[tex]B)\ x=43[/tex]
Step-by-step explanation:
One is given a circle with many secants within the circle. Please note that a secant refers to any line in a circle that intersects the circle at two points. A diameter is the largest secant in the circle, it passes through the circle's midpoint. One property of a diameter is, if a triangle inscribed in a circle has a side that is a diameter of a circle, then the triangle is a right triangle. One can apply this to the given triangle by stating the following:
[tex]x+47+90=180[/tex]
Simplify,
[tex]x+47+90=180[/tex]
[tex]x+137=180[/tex]
Inverse operations,
[tex]x+137=180[/tex]
[tex]x=43[/tex]
What are the zeros of , where
? help please need some help someone help please
[tex]{ \boxed{\boxed{\begin{array}{cc} \maltese \bf \: given \\ \\ \rm \: f(x) = ( {x}^{2} + 16)( {x}^{2} - 9) \\ \\ \bf \: for \: zeroes \\ \\ \pink{ \boxed{\boxed{\begin{array}{c | c} \bf \: {x}^{2} + 16 = 0 & \bf \: {x}^{2} - 9 = 0 \\ \\ = > {x}^{2} = - 16& {x}^{2} = 9 \\ \\ = > x = \pm \sqrt{ - 16} &x = \pm \: \sqrt{9} \\ \\ = > x = \pm \sqrt{ {i}^{2} {4}^{2} } &x = \pm \: \sqrt{ {3}^{2} } \\ \\ = > x = \pm \: 4i&x = \pm3 \end{array}}}} \\ \\ \rm \: x = \pm3 \: and \pm \: 4i\end{array}}}}[/tex]
Option A is the correct answer
the length of a mathematical text book the is approximately 18.34cm and its width is 11.75 calculate ?
the approximate perimeter of the front cover?
the approximate area of the front cover of the book?
Answer:
Perimeter=60.18cm
Area=215.495cm^2
Step-by-step explanation:
Given:
Length of book=18.34cm
Breadth=11.75cm
Solution:
Perimeter=2(l +b)
P=2(18.34+11.75)
P=2 x 30.09
P=60.18cm
Area=l x b
A=18.34 x 11.75
A=215.495 cm^2
Thank you!