Answer:
Proved , since LHS= RHS
Step-by-step explanation:
We need to prove the given expression ,
=> 1 + cos x / 1 + sec x = cos x
Simplifying LHS.=> 1 + cos (x) / 1 + sec (x)
=> 1 + cos (x) / 1 + 1/cos (x)
=> 1 + cos (x) ÷ 1 + cos(x) / cos (x)
=> 1 + cos (x) × cos(x) / { 1 + cos (x) }
1 + cos (x) gets cancelled . So we are finally left out with ,=> cos (x)
= RHS
Hence proved !In an all boys school, the heights of the student body are normally distributed with a mean of 70 inches and a standard deviation of 3 inches. What is the probability that a randomly selected student will be shorter than 63 inches tall, to the nearest thousandth?
The probability that a randomly selected student from the all-boys school will be shorter than 63 inches tall is approximately 0.9%.
To find the probability that a randomly selected student will be shorter than 63 inches tall, we need to use the standard normal distribution table or a statistical calculator.
Calculate the z-score for the value of 63 inches using the formula:
z = (X - μ) / σ
where X is the value (63 inches), μ is the mean (70 inches), and σ is the standard deviation (3 inches).
z = (63 - 70) / 3
z = -7 / 3
z = -2.3333
Now, we look up the area to the left of the z-score -2.3333 in the standard normal distribution table.
Using a standard normal distribution table, the cumulative probability for z = -2.33 (rounded to two decimal places) is approximately 0.009.
So, the probability that a randomly selected student will be shorter than 63 inches tall is approximately 0.009 or 0.9% (rounded to the nearest thousandth).
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6th grade math plsssssss whoever does this I will give any vbuck card, or Microsoft. PLSSS HELP!
Answer:
5 toppings
Step-by-step explanation:
$20 - $9 = $11 dollars left for toppings
$11 ÷ 2 = 5.5
So, you can get 5 toppings with 50 cents left.
Have a great day!
The area of the base of a rectangular prism is 40 squared inches. If the length of the prism is 4 inches, and the height of the prism is 5 inches, what is the total surface area of the rectangular prism
Answer:
220
Step-by-step explanation:
Which quadratic equation has roots of 5 and 7
Answer:
D
Step-by-step explanation:
Given the root of a quadratic equation x = a then the factor is (x - a)
Here the roots are x = 5 and x = 7 , then the corresponding factors are
(x - 5) , (x - 7)
The equation is then the product of the factors, that is
y = (x - 5)(x - 7) ← expand using FOIL
= x² - 7x - 5x + 35 ← collect like terms
y = x² - 12x + 35 → D
The quadratic equation has roots of 5 and 7 so, the quadratic equation would be equal to [tex]y = x^{2} - 12x + 35[/tex].
How to find the roots of a quadratic equation?Suppose that the given quadratic equation is
ax^2 + bx + c = 0
Then its roots are given as:
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
It is Given the root of a quadratic equation x = a then the factor is (x - a)
Here the roots are x = 5 and x = 7 , then the other factors are
(x - 5) , (x - 7)
The equation is then the product of the factors,
[tex]y = (x - 5)(x - 7)\\y = x^{2} - 7x - 5x + 35 \\y = x^{2} - 12x + 35[/tex]
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Which expresion is equivalent to -5 -(-7)?
HURRY 20 POINTS
Answer:
2 (the answer should have a positive sign.)The equivalent to -5-(-7) is -5+7.Step-by-step explanation:
To solve this problem, use the order of operations.
PEMDAS
Parentheses
Exponents
Multiply
Divide
Add
Subtract
[tex]\sf{-5-(-7)=-5+7}[/tex]
[tex]\sf{-5+7}[/tex]
Add or subtract.
Solve.
[tex]-5+7=2[/tex]
[tex]\large\boxed{2}[/tex]
So, the correct answer is 2.
Answer:3+(px6)
Step-by-step explanation:
Solve the given polynomial by factoring. Check all answers that are correct.
f(y) = 3y^3 + y^2 + 9y + 3
A) y = 1/3
B) y = i√3
C) y = 3
D) y = -3
E) y = -1/3
F) y = ±i√3
Which of the following do not represent the measures of the sides of a triangle?
A)57, 80, 24
B) 43, 133, 89
C) 5, 6, 7
D 20, 20, 30
===========================================================
Explanation:
For this answer choice, we have p = 43, q = 133, and r = 89. Note how p+r = 43+89 = 132, which is not larger than the third remaining side q = 133. Therefore, p+r > q is false and a triangle cannot be formed.
A triangle is only possible if and only if adding any two sides leads to a sum larger than the third side (triangle inequality theorem).
Put another way, we must have these three conditions hold true for a triangle to form:
p+q > rp+r > qq+r > pIf any of those three are false, then we cannot make a triangle with side lengths p,q,r
-----------------
Let's go over choice C for an example in which we can form a triangle
p = 5, q = 6, r = 7
We can see that,
p+q = 5+6 = 11 which is greater than r = 7. So p+q > r is true.p+r = 5+7 = 12 which is greater than q = 6. So p+r > q is true.q+r = 6+7 = 13 which is greater than p = 5. So q+r > p is true.All three conditions are true, and therefore we have a triangle that is possible with side lengths p = 5, q = 6, r = 7. I recommend cutting out slips of paper with these lengths to try it out yourself, so you have a real world example to play with. Choices A and D are a similar story to choice C, so we can rule out all three of these choices.
pls help fast i will give brainliest to the first answer i swear
Answer:
Green block= 5x5x5= 125 cm
Flat white block= 1x4x5= 20 cm
Standing white block= 9x3x7= 189 cm
Blue block= 3x4x2.5= 30 cm
The fridge= 174x57=9918 604998 divided by 9918 = 61 d= 61 cm
Step-by-step explanation:
complete the square f(x)=x^2-12x-4
Answer:
Solve for x over the real numbers:
x^2 - 12 x - 4 = 0
Add 4 to both sides:
x^2 - 12 x = 4
Add 36 to both sides:
x^2 - 12 x + 36 = 40
Write the left hand side as a square:
(x - 6)^2 = 40
Take the square root of both sides:
x - 6 = 2 sqrt(10) or x - 6 = -2 sqrt(10)
Add 6 to both sides:
x = 6 + 2 sqrt(10) or x - 6 = -2 sqrt(10)
Add 6 to both sides:
Answer: |
| x = 6 + 2 sqrt(10) or x = 6 - 2 sqrt(10)
Find the distance between the points (4,3) and (1,0).
Write your answer as a whole number or a fully simplified radical expression. Do not round.
units
Answer:
[tex]distance = \sqrt{(x_{1} -x_{2})^2+(y_{1} -y_{2})^2 }[/tex]
[tex]=\sqrt{(1-4)^2+(0-3)^2 } \\=\sqrt{3^2 + 3^2}\\=\sqrt{18}\\=3\sqrt{2}[/tex]
Answer:
3√2
Step-by-step explanation:
√(x2 - x1)² + (y2 - y1)²
√(0 - 3)² + (1 - 4)²
√(-3)² + (-3)²
√(9) + (9)
√18
3√2
does anybbody know the answer to this? #help
Answer:
each tube costs $1.5 so put it the point in between 1 and 2
thank you
Step-by-step explanation:
Use cosine law to find the value of x. Show working. use ^ for power and sqrt for square root
Answer:
x ≈ 11.89
Step-by-step explanation:
Using the cosine rule
x² = 4² + 9² - ( 2 × 4 × 9 × cos128° )
= 16 + 81 - 72cos128°
= 97 - (- 44.33 )
= 141.33 ( take the square root of both sides )
x = [tex]\sqrt{141.33}[/tex] ≈ 11.89 ( to 2 dec. places )
Correct I’ll give brainlist no links or I’ll report
Helpppp chile. I’m stuck sidnfifnfig vkfniffnf
Step-by-step explanation:
12*4 - 2*2
48 - 4
44 ft of carpet.
Ms Shepard cuts 1/2 of piece of construction paper. She uses 1/6 of piece of paper to make flower. This means that she used 1/12 of sheet of paper to make the flower. True or false
Answer:
true
Step-by-step explanation:
subject?
Name the integer that is 2 more than the opposite of -4.
Answer:
6
Step-by-step explanation:
the opposite of -4 is 4 and then add 2
Answer:
Yeah 6
Step-by-step explanation:
Exact same steps as the person above :)
Good luck!!
PLEASE HELP!
What is the equation of the directrix
for the following parabola:
(x - 1)^2 = 12(y + 2)
A. Y = -5
B. X = -5
C. y = -3
D. y = -12
Answer:
y=-5
Step-by-step explanation:
What is the solution?
-4(3) - 3 = ?
PLEASE HELP THANK YOU BRANLIEST IS PROVIDED
Answer:
Solution given;
area of semi circle=½πr²=1/2×3.14×4²=25.12in²
area of rectangle ABCD=l×b=8×13=104in²
area of rectangle CEFI=l×b=3×6=18in²
Total area =25.12+104+18=147.12in²
Area of circle
πr²π(7+6-5/2)²π(8/2)²16π25.12in²Area of centre rectangle
8(13)104in²Area of right rectangle
3(6)18in²Total
18+104+25.12122+25.12147.12in²You have an allowance to spend on lunch this
week. You will spend the same amount each
day, and you get to keep whatever is left at
the end of the week. After two days, you
have $12.10 remaining. After five days, you
have $2.50 remaining. what is the initial value, rate of change, and table of values
Answer:
look at the screenshot
Step-by-step explanation:
MRK ME BRAINLIEST PLZZZZZZZ
To find the quotient of 726.02 and 1,000, move the decimal point in 762.02___Places to the ____
Choices for blank 1.
A. 2
B. 3
C. 4
D. 5
Choices for blank 2.
A. Left
B. Right
NO LINKS!!
from blank one five
from blank two is right
Of 800 Participants in a marathon, 120 are running to raise money for a cause. How many participants out of 100 are running for a cause?
Answer:
15
Step-by-step explanation:
800 = 120
100 = x (number we have to find)
800x = 12000
x = 12000 ÷ 800
x = 15
PLS HELP ME WITH THIS QUESTION!!
Answer:
a
Step-by-step explanation:
Which two products can add to find 9 times 4?
Answer:
2x18=36
im not sure if that's what you meant but i can answer again if you want
Step-by-step explanation:
Answer:
sin ( 330 )
csc ( 60 )
cos ( 390 )
Step-by-step explanation:
Arnetta’s monthly gross pay is $4,200 federal withholding is 16.05%
Answer: $3204.06
Step-by-step explanation:
Here's the complete question:
Arnetta's monthly gross pay is $4,200. Federal withholding is 16.05% of her pay. Her other deductions total $321.30. Find her net pay.
First, we calculate the Federal witholding which will be:
= 16.05% × $4200
= 0.1605 × $4200
= $674.10
The total deduction will now be:
= $674.10 + $321.30
= $995.40
The net pay will now be:
= Gross pay - Total deductions
= $4,200 - $995.40
= $3204.06
Therefore, Arnetta’s net pay is $3204.06
Kaylee obtains a loan with simple interest to buy a car that costs $8,500. If Kaylee pays $1,020 in interest during the four-year term of the loan, what was the rate of simple interest?
Answer:
The rate is 3 percentage
Help
Please edge 21 I really need help I don’t want to go to summer school
Answer:
C. No solutions exist Because the situation describes two lines that have the same slope and different y-intercepts
Step-by-step explanation:
it is important to keep the x-and y-coordinates in the same order in both the numerator and the denominator otherwise you will get the wrong slope so there is no solution.
I needs your helps please :) ty
Answer:
so the answer could either be
Yes. as elevation increases, the temp decreases
but..
there is also no trend coz the points are scattered i.e the temp
as the elevation is increasing the temp does vary.
so My final answer would be no, there is not a trend
ASAP someone please help. Given the following angle measurements for a triangle, find the remaining angle.
a. 53, 58
b. 28, 47
c. 65, 25
Answer:
c
Step-by-step explanation:
4
Select the correct answer.
Which of the equations below represents a line parallel to the yaxis?
A. X= -y
B. X= 4y
C.x=y
D.X= 4
HELP
Answer:
x=4
Step-by-step explanation:
The y axis is a line where the value of x does not change ( x=0)
It is a vertical line
The only line where the value of x does not change is x=4
It is a vertical line at x=4